Entwistle quit on November 11 after a Newsnight report - aired nine days earlier - led to Lord McAlpine being wrongly linked to child abuse on the internet.
[Left: Lord Patten / Right: George Entwistle]
His rocky reign also included another controversy involving a dropped Newsnight investigation into sex abuse allegations against former BBC star Jimmy Savile last year.
There has been criticism of the £450,000 pay-out for Entwistle's departure, which was double the figure permitted for a resignation in his contract.
Appearing at the Commons culture, media and sport, select committee, Lord Patten agreed that the amount was a 'hell of a lot of money', but said that he had been given little other option at a meeting with Entwistle before he resigned as director general.
He said that Entwistle had asked if the BBC Trust was "urging him to go", but was told: "We are not urging you to go, but we are not urging you to stay."
In the negotiation that followed, Entwistle's lawyers were said to have insisted that he receive a full 12 months' salary, despite serving just 54 days in the job.
If this pay-off was refused, then the lawyers said that Entwistle could go to an industrial tribunal and could have won an additional £80,000 on top of the £450,000.
"We did not have grounds for dismissal," Lord Patten said. "We could either accept a consensual deal for 12 months, or the situation would drift on and we would find ourselves with a constructive dismissal (claim) and also an unfair dismissal."
Lord Patten, a former Tory MP, dismissed any suggestion that he was not aware of the political fallout of the pay-off.
He also said that the BBC could "claw back" some of the money if Entwistle was found to have done anything wrong in the two inquiries into Savile's time at the BBC and the Newsnight controversy.
But despite the criticisms of Entwistle, Lord Patten said that he would not "trash a decent man" who had been "overwhelmed" by events.
He said that there had never before been an occasion when a BBC director general had been "swept away by a terrible failure of journalism".
"[I] wondered by the end of it how much his heart was in it," said Lord Patten. "I think he found the whole thing an appalling experience."
[Lord Tony Hall]
Lord Patten said that the BBC needed a "belt and braces" approach to make sure such "shoddy journalism" as the Newsnight report was not repeated.
But he added: "The BBC must not abandon or resign from investigative journalism. It's important that your journalistic standards are even higher for investigative journalism."
Also appearing in front of the MPs today, acting BBC director general Tim Davie said that the BBC was not "falling apart", despite staff being "aghast at the failings" in Newsnight report, aired on November 2.
Davie, who will become the chief executive of BBC commercial arm BBC Worldwide next year, said of the report: "It was a bad editorial mistake and there will be consequences."
He told the committee that the Pollard review into the dropped Newsnight investigation into the Savile allegations had cost £200,000 in legal costs so far. It is expected that this will be completed by Christmas.
Lord Tony Hall, the current chief executive of the Royal Opera House, is to become the next permanent director general of the BBC in March 2013.