The former deputy Labour leader cautioned her party's MPs from seeking to replace the prime minister following the loss - and insisted it "could be worse".
Green Party candidate Hannah Spencer won the by-election with 14,980 votes - a majority of 4,402 - in the early hours of Friday morning, pushing Labour into third place in an area they have not lost since 1931.
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But speaking to the Electoral Dysfunction podcast, Baroness Harman insisted "it would've been worse if it had been Reform" who won, and urged Labour backbenchers to hold their resolve.
She told Sky News' political editor Beth Rigby: "This has been very painful and bruising, it will increase anxiety in the run-up to the council elections in England, and in elections in Scotland and Wales.
"This will test the mettle of the PLP [Parliamentary Labour Party], they don't want instability. They do want delivery on the manifesto.
"But the fundamentals remain absolutely the same - that piling instability into this situation by having a leadership challenge is not going to solve the problems that people want solved, which is improvement in the way their lives are, improvement in their public services and stability in government."
The Labour peer also sought to play down Labour's by-election loss, by saying a Reform UK victory would have "really scared me".
She explained: "I would've felt worse if Reform had won because if you feel that this country is moving towards really quite divisive, racist, xenophobic, populist right-wing policies - that would've really scared me.
"It was very bruising and disappointing that Labour, having hope to win, didn't win. But I would've felt much worse if Reform had won."
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However, Baroness Harman conceded: "It's not a good day, no doubt about it.
"But, I mean, it's not... I don't want to sound pollyannaish, but it could be worse.
"A lot of people will be feeling, 'no, it couldn't be worse'. But actually, as far as I'm concerned, it would've been worse if it had been Reform."
Sir Keir is expected to speak to journalists later on Friday morning, where he will give his first on-camera reaction to the by-election loss.
Gorton and Denton has historically been considered to be a safe seat for Labour, and it was the party's 38th safest seat in the 2024 general election.
The result in the Greater Manchester constituency is Labour's seventh-worst by-election defeat in history.
One Labour MP told Sky News' deputy political editor Sam Coates that Sir Keir should resign following the loss, while a number of Labour backbenchers have publicly called for "change at the top", either in the form of the PM's departure or a change of direction.
Long-time critic of the Labour leader, Brian Leishman, Labour MP for Alloa and Grangemouth, wrote on social media: "The blame lies with Starmer & the people that surround him.
"The political idea that we should try & out-Reform Reform is wrong and been rejected.
"Time he did the right thing for the country & the Labour Party, and go."
Andy McDonald, Labour MP for Middlesbrough and Thornaby East, said: "It is the political approach of the prime minister, his former chief of staff and of Labour Together which has cost Labour this safe seat.
"The party must rip up their approach if Labour is to convince the public that the change they demand is going to be delivered."
His colleague, Nadia Whittome, MP for Nottingham East, said it "is those running our party who are to blame" and that "serious lessons need to be learnt".
But Transport Secretary Heidi Alexander defended the government, telling Sky News it was a "deeply disappointing" result, but adding: "I don't think we should over-interpret this result."
A 38-year-old man has been arrested on suspicion of racially aggravated criminal damage and remains in custody.
A No 10 spokesman said: "It's obviously a disgrace. It's completely abhorrent.
"Churchill was a great Briton. This Government will always stand up for our values and the perpetrator must be held to account.
"We're glad the police have made an arrest."
Officers from the Metropolitan Police were alerted to the vandalism shortly after 4am on Friday.
Other phrases including "Stop the Genocide" and "Free Palestine" were sprayed in red paint on the bronze sculpture.
Further graffiti read "Never again is Now" and "Globalise the Intifada".
Dutch group Free the Filton 24 claimed responsibility for the action on Friday morning.
It posted a video on its Instagram account appearing to show a man dressed in red coveralls, with "I support Palestine Action" written on the back, painting the statue.
Free the Filton 24 defines itself as a group of "family and friends" of the 24 Palestine Action activists who were charged over a break-in at one of Israel-based defence firm Elbit's UK sites in 2024.
Olax Outis, who said he is Dutch and part of the group, has claimed to be the man on the statue.
In a statement on its Instagram account, Mr Outis said he defaced the statue "to draw attention to the horrible human rights violations happening in a country that's run by colonisers who refuse to listen to their people".
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The statue has been cordoned off and was being cleaned this morning.
A Greater London Authority spokesperson said: "We are appalled by this vandalism to the statue of Sir Winston Churchill and work is under way to remove the graffiti as quickly as possible."
Commenting on an image of the monument, which was shared on X, Dave Rich, director of policy for Community Security Trust, posted: "Free Palestine" and a Hamas red triangle, if you zoom in close enough. This extremism is never just a threat to Jews."
The Jewish Leadership Council said it was "disgusted" by the defacing of the statue.
It said on X: "In targeting the statue of a British hero who led this country in the fight against the Nazis, the perpetrator has found a perverse way to combine a hatred of Jews with a disdain for Britain."
Phil Rosenberg, president of the Board of Deputies of British Jews, wrote: "One of the greatest champions for liberty, who defeated the Nazis, defaced.
"Zionism, the national liberation movement of the Jewish people, inverted.
"Santayana's 'Those who cannot remember the past are condemned to repeat it', never truer."
The 12ft-tall statue on the north-east corner of the square, created by Ivor Roberts-Jones, was unveiled in 1973 by the former prime minister's wife, Lady Clementine Churchill.
It is one of 12 statues on or around Parliament Square, most of well-known statesmen such as Nelson Mandela and Abraham Lincoln.
The former prime minister's statue has been vandalised several times over the years, including during demonstrations.
Last December, both the Metropolitan Police and Greater Manchester Police announced anyone chanting "globalise the intifada" would face arrest.
The decision by the two police forces came in the wake of the Bondi Beach terror attack, and the terror attack at Heaton Park synagogue in Manchester on 2 October.
The Soham murderer, 52, was taken to hospital after being found in a pool of blood following an alleged attack by an unknown inmate on Thursday.
A Durham Constabulary spokesperson said: "There has been no change in the 52-year-old man's condition overnight - he remains in hospital in a serious condition."
Police earlier said that a man in his mid-40s was being investigated over the incident.
"He has not been arrested at this stage but remains in detention within the prison," a spokesperson added.
Huntley was convicted of the murders of 10-year-olds Holly Wells and Jessica Chapman in Soham, Cambridgeshire, in 2002.
The latest incident is not the first time Huntley has been attacked at HMP Frankland.
In 2011, an inmate who slashed Huntley's throat with a makeshift knife was jailed for life.
Damien Fowkes was sentenced to a minimum of 20 years for the attempted murder of Huntley in March 2010 and the manslaughter of child killer Colin Hatch.
Fowkes inflicted a wound seven inches long on the Soham murderer's neck and the court was told it was only "good fortune" that the weapon missed anything vital.
The disappearance and murders of the two 10-year-old schoolgirls captured the attention of the nation in 2002.
Huntley killed them in August of that year after they left a family barbecue to buy sweets, and then dumped their bodies in a ditch.
He was their school caretaker and put himself forward as a volunteer to help search for them after they went missing - and was interviewed by reporters on camera.
The efforts to locate the girls in the 13 days after they disappeared have been described as one of the most intense and extensive in British criminal history.
Huntley was convicted of the murder of both girls in December 2003 and sentenced to two terms of life imprisonment.
His girlfriend, Maxine Carr - the girls' teaching assistant - had knowingly provided Huntley with a false alibi.
She received a three-and-a-half year prison sentence for conspiring with Huntley to pervert the course of justice.
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Mr Wallace was suing the broadcaster and its subsidiary BBC Studios Distribution Limited for up to £10,000 in damages, alleging the BBC failed to disclose his personal data, which caused him "distress and harassment".
The BBC was defending the claim and denied Mr Wallace had "suffered any distress or harassment", stating in court documents he was not "entitled to any damages".
The former MasterChef presenter was sacked last July following an investigation into misconduct allegations.
A BBC spokesperson confirmed on Friday that Mr Wallace had abandoned the claim.
They said: "Shortly in advance of a hearing, due February 16, Mr Wallace discontinued his claim.
"He is not receiving any payment in costs or damages from either BBC or BBC Studios."
He began co-presenting MasterChef in 2005, but it was announced in November 2024 that he would step away from his role while the misconduct allegations were investigated.
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A review by law firm Lewis Silkin later upheld 45 of the 83 allegations against him, including one of "unwelcome physical contact".
Mr Wallace issued an apology, saying he was "deeply sorry for any distress caused" and that he "never set out to harm or humiliate".
Mr Wallace has been approached for comment.
He said the US has the power to end the war - but must exert greater pressure on Moscow.
"The United States even more stronger than they think about themselves. And I think so really. And they really have pressure on Putin. They can stop this war."
But he urged the administration in Washington to tighten sanctions against the families of Russia's leadership and to provide Ukraine with more advanced weapons, arguing that only increased pressure would force Moscow to take negotiations seriously.
On the question of how close Ukraine is to reaching peace he says there is a window between now and the American midterm elections in November.
"Now I think that we have a chance. Between us, what I really think about next year… it depends on these months, if we will have a chance to finish the war before autumn. Before elections, important, influential, elections in the United States. If it will be possible to achieve a peace, we will have, now we have this window."
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I spoke to him for an hour at the presidential buildings in Kyiv about what Ukraine needs now - and what must happen for the war to end.
More than four years after Russia launched its botched full-scale invasion, the toll on the country - and on him and his family - is unmistakable.
As we walked through near darkness to the room where the sit-down interview was held, he spoke about the strain of rolling power cuts and entire regions enduring temperatures as low as -40 degrees without reliable heating.
When I asked whether Ukraine could win the war, his answer was equivocal.
"It depends what people mean when they say, to win. And, really it's very difficult to speak about territories. First of all how to get back all of the land for today, it's very difficult. And it will be too much losses (of) people lives… But what is good that Russia also can't do it on the battlefield. So that's why they're not winning and we are not losing."
But on the question of surrendering the fortress cities of Sloviansk and Kramatorsk, he was unequivocal - that would be a red line.
"It's our territory and it sounds unbelievably strange why we have to withdraw from our land? Why they occupied it, our land and nobody can push them out."
"If we will withdraw from this territory, like you said, for example, Sloviansk at the very moment, at this very moment, 200,000 people who are there now will be occupied by the Russians, who said to Russia that these people are ready to be Russian people? And if they don't, they will kill them or push to the front or push to the prison."
Zelenskyy also spoke openly about his relationship with Donald Trump, describing it as "not simple" but stressed that Ukraine's relationship went beyond "personalities".