All 12 men arrested over a suspected bomb plot in the UK have now been released without charge by police.
Eleven - all Pakistani nationals - have been transferred to UK Border Agency custody and face possible deportation.
Chief Constable of Greater Manchester Police Peter Fahy defended the inquiry, saying he was not "embarrassed".
But the Muslim Council of Britain said the government should admit it had made a mistake and claimed the way it had dealt with the men was "dishonourable".
Prime Minister Gordon Brown's spokesman told reporters: "We are seeking to remove these individuals on grounds of national security.
"The government's highest priority is to protect public safety. Where a foreign national poses a threat to the country, we will seek to exclude or deport them where appropriate."
However, lawyers for the men point out that they have not been charged and are innocent of any crime.
Of the 12 men arrested in raids in Liverpool, Manchester and Clitheroe in Lancashire, 11 were Pakistani nationals, with 10 holding student visas. One was from Britain.
The Crown Prosecution Service (CPS) decided there was insufficient evidence to press charges - or even to convince magistrates to allow police to hold the men any longer.
Greater Manchester Police led the inquiry and Mr Fahy said: "I do not believe a mistake has been made.
"I do not feel embarrassed or humiliated about what we have done. We carried out our duty."
Dominic Casciani, of the BBC's home affairs team
If someone is arrested on suspicion of a crime, they either end up in the dock or walking out of the police station a free man.
But for foreign nationals accused of crime there is a third way - being sent directly for immigration removal.
The home secretary has considerable powers to deport foreign nationals whose presence is not conducive to the public good - and she doesn't need hard criminal evidence to go ahead.
The cases will go to the Special Immigration Appeals Commission, effectively a national security tribunal.
It can hear evidence in secret - which means that intelligence assessments with no weight in a criminal trial can be used to ban someone from the UK.
That means that we're unlikely to ever hear the full story - and if the men lose, the security services can say they acted appropriately.
It boils down to the difference between whatever the secret intelligence police and security services believed they had uncovered and the lack of evidence that the men were doing anything illegal.
He added the fact the raids had to be brought forward after Metropolitan Police Assistant Commissioner Bob Quick accidentally revealed secret documents to photographers had not affected the outcome.
Metropolitan Police Commissioner Sir Paul Stephenson added: "I am satisfied that the action taken was the right action taken and we now have to follow the proper legal process."
Mr Fahy said both the Muslim community and public at large understood the threat to the UK and that police would sometimes arrest people without pressing charges afterwards.
Other people were free to speculate that a terrorist plot had been foiled following the raids but the police's duty was to protect the public and gather evidence, he added.
Lawyer Mohammed Ayub, who is representing three of the men, said in a statement: "After 13 days in custody, during which no evidence of any wrongdoing was disclosed, they have now been released without charge.
"Our clients have no criminal history, they were here lawfully on student visas and all were pursuing their studies and working part-time. Our clients are neither extremists nor terrorists."
Inayat Bunglawala, of the Muslim Council of Britain, said the government had been "dishonourable" over the way it had dealt with the men.
Mr Bunglawala told the BBC that when the arrests "took place in very dramatic circumstances of students being pulled out of university and thrown to the floor" the public had been assured the men posed a serious threat.
He said it was unacceptable for the government to make these sorts of prejudicial remarks from the outset and then, having found insufficient evidence to bring charges, to deport the men anyway.
"Politics should not be interfering with what is primarily a legal process," he said.
"What we don't want is people becoming cynical as a result of politician's premature remarks and thinking: 'well, that's what they said last time'."
Liberal Democrat home affairs spokesman Chris Huhne described it as "yet another embarrassment" for Home Secretary Jacqui Smith.
"Serious questions need to be answered about whether Bob Quick's blunder distorted this operation and on what grounds these men are being deported," he said.
BBC security correspondent Gordon Corera said: "I think there will be a sense of a need to learn some lessons from this is in terms of public presentation."
Assistant Commissioner Quick - the UK's most senior counter-terrorism officer - quit his post a day after the operation.
However, the home secretary told MPs on Monday the error had not damaged the operation and the only impact had been that the raids had been brought forward "by a matter of hours".
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