Theresa May was forced to go to the Commons to make a statement after shadow home secretary Yvette Cooper tabled an emergency question.
Mrs May told MPs the appeal had been lodged by Qatada's lawyers after the deadline had passed at midnight on Monday.
She dismissed suggestions that the Home Office had miscalculated the date.
"The Government is clear that Abu Qatada has no right to refer the case to the Grand Chamber of the European Court of Human Rights (ECHR), since the three-month deadline to do so lapsed at midnight on Monday," she said.
"The Government has written to the European Court to make clear our case that the application should be rejected because it is out of time."
Qatada remains in custody and the Government would resist "vigorously" any bail application, she said.
Lawyers for the radical cleric lodged an appeal with Europe's human rights judges following his latest arrest on Tuesday, effectively putting moves to return him to stand trial in his native Jordan on hold.
However, after the court refused to confirm the Home Office had calculated the deadline correctly, Ms Cooper called on Mrs May to return to the Commons to explain what had happened.
A miscalculation of the deadline would be a massive embarrassment for Mrs May and could again set back the authorities' long-running battle to put Qatada on a plane out of the country.
Ms Cooper said in the Commons: "When the Home Secretary is accused of not knowing what day of the week it is, then chaos and confusion has turned into farce."
She demanded to know whether the Home Office had clarified the deadline prior to the appeal being lodged, to which Mrs May replied: "Of course the Government were talking to the European court throughout the three months and we were talking to them on the basis that the deadline was April 16."
Mrs May, who earlier described the appeal by Qatada's lawyers as a "delaying" tactic, acknowledged that the court could find that the deadline was midnight on Tuesday - as Qatada's lawyers argued - an hour after the appeal was lodged.
"It is a judgment that is going to be made by the panel of the Grand Chamber. They are the only final arbiters of what the deadline was," she said.
When pressed by Labour former home secretary Alan Johnson, she said that if the Government were to be found to be in error, she would take full responsibility.
A spokeswoman for the Strasbourg-based court said Qatada's appeal was lodged at 11pm local time (10pm BST) on Tuesday, but added: "We cannot comment on the view taken by the UK authorities about when the deadline expired."
Justice Secretary Ken Clarke told Sky News he believes Mrs May has every reason to be confident in her decision.
He was speaking in Brighton where he is hosting a conference of representatives from the 47 member nations of the Council of Europe aimed at reforming the ECHR and the types of cases it hears.
Mr Clarke told Sky: "I'm sure the Home Office lawyers will sort it out. It's not unusual in a case to begin with a procedural wrangle."
Prime Minister David Cameron has expressed his determination that Qatada will eventually be deported.
"I am absolutely clear, the entire Government is clear, and frankly I think the country is clear, that this man has no right to be in our country," he said on Wednesday.
The latest appeal is separate from any others Qatada's legal team may make over the decision by Mrs May to continue with his deportation after receiving assurances from Jordan that evidence gained through torture would not be used against him.
Instead it relates to a strand of the original decision of the Strasbourg-based court which found that the 51-year-old could be sent back to Jordan with diplomatic assurances that he would not be tortured.
He is currently detained after a judge ruled his imminent deportation meant the risk he could try to flee while on bail had increased.
His lawyers have said they will challenge all moves to deport him and Mrs May has warned MPs that it may still be "many months" before Qatada can be lawfully expelled from the UK.
Qatada, who is said to have "wide and high-level support" among extremists, was convicted in his absence in Jordan of involvement with terror attacks in 1998 and now faces a retrial there.