Greg Dyke has said Lord Hutton was "quite clearly wrong" on some points of law in his report.
Hundreds of BBC staff mobbed Mr Dyke
The departing BBC director general told GMTV Alastair Campbell had been "ungracious" in the aftermath of the report.
Mr Dyke said he would be interested to know what other law lords might think of Lord Hutton's conclusions on the death of Dr David Kelly.
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.
"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 told BBC Radio 4's Today programme: "I think 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."
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."
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."
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.
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
It would have been easy 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 said: "He has been remarkably ungracious."
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".
His comments came as ministers 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."