The comments came after the Home Secretary had taken full responsibility for farcical scenes that resulted in the radical cleric's removal to Jordan being halted.
Qatada's lawyers have claimed the Government was wrong in regards to when he could be arrested.
David Cameron attempted to draw a line under the row, saying he wished he could "put him on a plane myself".
The Prime Minister said ministers would continue trying to remove Qatada "however long it takes".
During a stormy session in the House of Commons yesterday, Mrs May told MPs her department had not made a mistake.
Qatada's arrest on Tuesday, at the same time as the Coalition announced a deal with Jordan that would pave the way for his deportation, had been ordered only after the deadline for him to launch legal appeal had expired, she insisted.
However, she admitted the Government had ignored warnings it had got the wrong date.
Within hours she suffered a blow when the Council of Europe appeared to agree that the Home Office had indeed miscalculated the deadline.
Advice from the council said Qatada's appeal against deportation, lodged on Tuesday night, may have been submitted "just in time".
Judges will still have to rule on the exact timing, and if they will hear his appeal.
However, the move will lead to further delays in attempts to deport Qatada, which began in 2002, and may result in the terror suspect being released on bail.
Grilled by MPs, Mrs May admitted to the House of Commons there had been warnings on Monday the UK Government could have got the date wrong.
Labour accused her of failing to deny she had received advice to delay any arrest for 24 hours to err on the sided of caution.
Ex-Labour home secretary Alan Johnson said that it would have been sensible to wait until Wednesday to order the arrest.
Labour's Shadow Home Secretary Yvette Cooper mocked Mrs May for "partying with X Factor judges" after photographs appeared of the minister at a social event on Tuesday night while Qatada's lawyers were busy submitting their appeal.
Tory MPs urged Mrs May to deport the terror suspect as soon as possible, even if it meant defying European law.
Veteran Conservatives also called on the Coalition Government to drop the European Convention on Human Rights.
Mr Cameron was among those who voiced their frustration.
During a visit to Bellshill in North Lanarkshire, he said: "However long it takes and however many difficulties there are, we will get him out. I sometimes wish I could put him on a plane and take him to Jordan myself.
"But the Government has to act within the law. That is what we'll do. We will get this done."
The final decision on whether the appeal is admissible rests with a panel of five judges from the court's Grand Chamber.
Mrs May will face further questioning on the issue by MPs on the Commons Home Office committee on Tuesday.
The row comes as the Government is attempting to convince other countries in European to reform the court of human rights. It says the number of cases it hears must be narrowed amid concerns the balance of power between the court and national parliaments is skewed.