Liberal Democrat home affairs spokesman Chris Huhne said: "I certainly think that his credibility - for anybody who sees the show - is going to be seriously damaged by his performance."
Mr Griffin told BBC News too much of the programme had been a "beat up Nick Griffin programme instead of Question Time".
He added that of the 25 or so allegations made against him in the programme - he was only allowed to answer four or five of them and that was "grossly unfair".
And a BNP spokesman complained that the programme had focused entirely on Mr Griffin's views and ignored newsworthy stories such as the postal strike, Afghanistan and Europe.
"This was not a normal Question Time," he told BBC Radio 4's Today programme. "It was 'let's have a go at Nick Griffin time'."
The BNP leader was booed at the start of the recording and accused of trying to "poison politics" as he was attacked by fellow panellists and the audience.
During the show the panel covered topics including whether it was fair for the BNP to "hijack" images of Winston Churchill, whether immigration policy had fuelled the BNP's popularity and whether Mr Griffin's appearance was an early Christmas present for the party.
He was asked by a member of the audience about why he had described Islam as a "wicked and vicious faith".
Mr Griffin said the religion had its "good points... it wouldn't have let the banks run riot" but it did not fit in with "the fundamental values of British society, free speech, democracy and equal rights for women".
He was scrutinised and challenged along with the other panellists heavily by the audience, that was right in our view
His references to Britain's "indigenous people" prompted other members of the panel to challenge him to say he meant white people.
Mr Griffin said the colour was "irrelevant" and said Mr Straw would not dare go to New Zealand and tell a Maori he was not "indigenous". "We are the aborigines here," he claimed.
Mr Straw said what distinguished the BNP from other parties was that other parties "have a moral compass... Nazism didn't and neither I'm afraid does the BNP."
The BNP leader insisted his views had been widely misrepresented in the media and denied a string of statements attributed to him, including a quote from 2006 in which he said "Adolf went a bit too far".
"I am not a Nazi and never have been," he said, adding: "I am the most loathed man in Britain in the eyes of Britain's Nazis."
He admitted sharing a platform with former Ku Klux Klan leader David Duke - but described him as "always totally non-violent".
He said he had been trying to win over "youngsters" Duke was trying to "lead astray".
Challenged on his views on civil partnership, he said: "I said that a lot of people find the sight of two grown men kissing in public really creepy. I understand that homosexuals don't understand that but that's how a lot of us feel, Christians feel that way, Muslims, all sorts of people."
Asked about a quote attributed to him in which he equated six million deaths in the Holocaust with the flat earth theory he replied that "European law" stopped him explaining.
"I can't tell you why I used to say those things anymore than I can tell you why I have changed my mind," he said.
The justice secretary said when anybody put a specific quotation to Mr Griffin he tried to "wriggle out of it".
If Nick Griffin's appearance on Question Time has the ultimate effect of shaking the 'great' british public free of their political apathy and encourages them to ask probing questions, then his appearance will be a good thing
Asked whether immigration policy had fuelled the BNP, Mr Straw said he did not think it had and said he thought the BNP had been boosted by discontent with the main parties over issues like expenses.
But Baroness Warsi said politicians had a responsibility to take on the BNP on the issue of immigration: "Many people who vote for the BNP are not racist and therefore what we have to do is go out and say to these people as mainstream political parties we are prepared to listen."
Mr Griffin blamed the "political elite" for imposing "an enormous multicultural experiment on the British people".
But Mr Griffin was challenged by several black and Asian members of the audience.
One man asked Mr Griffin: "Where do you want me to go? I love this country, I'm part of this country."
While the programme was being recorded the anti-BNP protest continued. The Metropolitan Police say six protesters were arrested and three police officers injured in the protests.
Mr Griffin accused the protesters of "attacking the rights of millions of people to listen to what I've got to say and listen to me being called to account by other politicians".
Protesters storm into BBC Televison Centre
But Weyman Bennett from Unite Against Fascism accused the BBC of "rolling out the red carpet" to Mr Griffin and said his appearance on the flagship discussion programme "will lead to the growth of a fascist party" and promote violence against ethnic minorities.
About 25 people managed to get through the gates and run towards the BBC building when security guards opened them to let in a car. A few minutes later they were led, dragged or carried back outside.
There were also protests outside BBC buildings in Bristol, Liverpool, Nottingham, Glasgow and Belfast.
Welsh Secretary Mr Hain, who had tried to stop the broadcast, said: "The BBC should be ashamed of single-handedly doing a racist, fascist party the biggest favour in its grubby history."
BBC Deputy Director General Mark Byford said it had been "appropriate" to invite Mr Griffin to appear given the support the BNP received in the last European elections when it gained its first Euro MPs.
He said: "He was scrutinised and challenged along with the other panellists heavily by the audience, that was right in our view.
"It would have been quite wrong for the BBC to have said 'yes, you are allowed to stand in elections, yes you have a level of support that now meets the threshold but the BBC doesn't think that you should be on'."
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