The BBC has taken legal advice on whether it can recoup some of the £450,000 pay-off given to director-general George Entwistle, Lord Patten said.
But the chairman of the BBC Trust said he doubted a bid to get some of the money back would be successful.
The corporation has been accused of a "cavalier" attitude towards licence fee money over the pay-off. Mr Entwistle resigned after just 54 days in the job as a result of his handling of the fallout from the Jimmy Savile crisis, and was paid the money - twice the amount to which he was entitled - in order to speed up his departure.
A report by the Public Accounts Committee was scathing, saying it was "out of line both with public expectations and what is considered acceptable elsewhere in the public sector". It said further benefits paid to him were "an unacceptable use of public money". MPs also criticised "excessive" severance payments to 10 other senior managers, including former chief operating officer Caroline Thomson who received £670,000 when she left this year.
The report is the latest blow to the BBC, after a review by former Sky News executive Nick Pollard - published on Wednesday - painted a picture of a top-down organisation beset with rivalries and faction fighting. It found the decision to drop a Newsnight report into Savile's decades-long campaign of sexual abuse plunged the BBC into "chaos and confusion", revealing a corporation where "leadership and organisation seemed to be in short supply".
Lord Patten said: "We've taken legal advice about whether we could actually take any money back. In order for us to do so we have to be able to argue that, on the basis of what Pollard says, it would have been justified to make a summary dismissal of the former director-general and I rather doubt whether we will get the legal go-ahead for that."
He said that with "hindsight" the Trust chose the wrong candidate for the top job, and said if the BBC had refused Mr Entwistle's pay-off claim it would have ended up in "an appalling mess" in the courts
Margaret Hodge, who chairs the committee, warned out-of-touch BBC executives risked inflaming "dangerous" calls for the broadcaster to be subject to more political oversight. She said: "I don't think the BBC gets it and doesn't understand public opinion."
Asked about the BBC's handling of Mr Entwistle's resignation, David Cameron's official spokesman said: "The Prime Minister's view is that BBC appointments are a matter for the BBC.
"It is for the BBC to justify it. At the time, the Secretary of State in the House made a parliamentary statement saying it was hard to justify the level of severance money agreed, but it is absolutely for the BBC to justify. The BBC on this is accountable to its licence fee-payers. The BBC Trust is there to ensure that the BBC takes these sorts of issues into account."