Greg Dyke has said he is shocked by the findings of the Hutton report and that all parts of the media should be concerned by its implications.
Hundreds of BBC staff mobbed Mr Dyke
The departing BBC director general said the report into the death of Dr David Kelly had been read with "disbelief".
Mr Dyke made it clear he did not accept all the report's findings, and attacked Alastair Campbell as "ungracious".
He admitted making mistakes in the way he responded to the government's original complaints.
But he said the concerns of whistleblowers in government and elsewhere had to be reported by the media.
Mr Dyke told BBC Radio 4's Today programme: "It is perfectly fair for you to draw the conclusion that I don't accept all of the report.
"Our legal team were all very surprised by the nature of the report.
"I think it was Stewart Purvis, the former chief executive of ITN, who said... it is remarkable how he has given the benefit of judgement to virtually everyone in the government and no-one in the BBC."
Mr Dyke suggested the implications for journalism coming from the report were a matter of grave concern for the media.
"Lord Hutton does seem to suggest that it is not enough for a broadcaster or a newspaper... to simply report what a whistleblower says because they are an authoritative source. You have to demonstrate that it is true. That would change the law in this country."
He said he had had to offer his resignation after the report but had not wanted to go.
"I said I couldn't stay here if I haven't got the support of the governors."
'Matter should rest'
But Constitutional Affairs Secretary Lord Falconer told Today the Hutton report had been "fair".
"Lord Hutton has made a very thorough investigation into what happened and I
think all of us have to reflect very carefully on what he has found."
The prime minister's official spokesman echoed Lord Falconer's views, saying: "A dispassionate judge has looked at the facts and has made his judgment on
the facts. That's where the matter should rest.
"We accept there was a lot of emotion and a lot of anger yesterday but the
judge has reached his conclusions on his assessment of the facts and what people
should recognise is that this is the judge's verdict."
But Lord Hutton was "quite clearly wrong" on some points of law in his report, Mr Dyke said.
Mr Dyke said there should be no more resignations at the BBC, insisting: "The crisis went away yesterday when I resigned, when the prime minister accepted that was the end of it."
The corporation had apologised before the report for a whole range of things and said one of the mistakes was not to launch an internal inquiry at the time of Mr Campbell's original complaint, Mr Dyke added.
"He was running a campaign to try to influence the BBC's coverage of the war. There was nothing wrong with that," he said.
But the former director general pointed out that a range of letters of complaint had been received at the time.
It would have been easy for some to think of it as "just another rant from Alastair Campbell".
Questioning "remarkable contradictions" between evidence given by the former Downing Street director of communications to the Foreign Affairs Select Committee and to Lord Hutton, Mr Dyke also told GMTV he thought Mr Campbell has been "remarkably ungracious".
Mr Dyke said he would be interested to know what other law lords might think of Lord Hutton's conclusions.
He said: "We were shocked it was so black and white."
"We knew mistakes had been made but we didn't believe they were only by us," he continued.
He said he agreed with departing BBC chairman Gavyn Davies that one could not "choose the referee" and had to accept his decision, but joked: "The government did choose the referee."
He added: "I would be interested in what a few other law lords, on looking at Hutton, thought of it.
September 2002: Government produces dossier about alleged Iraqi weapons of mass destruction, including claim they could be deployed within 45 minutes
May 2003: BBC Today programme's Andrew Gilligan broadcasts report of claims Downing Street "sexed up" dossier, with 45 mins claim included against intelligence agencies' wishes
10 July 2003:Dr David Kelly named as suspected source of report as government continues to deny the story
17 July 2003: Dr Kelly found dead
August 2003: Lord Hutton begins six weeks of hearings about the circumstances around Dr Kelly's death
"We have an opinion... there are points of law in there where he is quite clearly wrong. That doesn't mean to say he is wrong, that is an opinion."
Mr Dyke also questioned Lord Hutton's conclusion that the MoD had properly cared for Dr Kelly, telling GMTV: "If that's showing a duty of care I'm glad I don't work there."
On the spontaneous demonstrations of support by BBC staff, Mr Dyke said it made him feel like a "mixture between a politician and Madonna".
New acting director general Mark Byford is leading an internal inquiry into what went wrong at the BBC and the steps needed to ensure it does not happen again.
BBC director of news Richard Sambrook has sent an email to all staff saying he will be working with Mr Byford, senior editors and news managers to look at ways to rebuild trust in the corporation.
Meanwhile ministers have stressed the importance of a BBC independent of government influence in the wake of Lord Hutton's criticisms of the corporation.
Culture Secretary Tessa Jowell said: "A BBC that is nobody's lapdog, that challenges government and raises debate - that is in all our interests."