Lord Patten said Mr Entwistle - who dramatically resigned last night - had been "destroyed" by the botched Newsnight investigation which wrongly implicated a senior former Tory in a child abuse scandal.
However, he made clear that he would resist calls to follow suit, insisting his job was to ensure the BBC learned the lessons from what happened and from the inquiries under way into the Jimmy Savile child abuse scandal.
"I think that I now have to make sure that, in the interests of the licence fee payer and the audience, that the BBC has a grip, that we get ourselves back onto the road," he told BBC1's Andrew Marr Show.
"I think that my job is to make sure that we learn the lessons of those inquiries and that we restore confidence and trust in the BBC. If I don't do that then I am sure that people will let me know."
Lord Patten said he would be meeting with Tim Davie, the acting director-general of the BBC, today to discuss the future of the flagship programme.
Asked whether Newsnight could now survive, he told Sky's Murnaghan programme: "That's one of the things we will be discussing with the acting director-general today.
"I think one of the things that should survive is the investigative journalism which it has represented along with Panorama. At the heart of our news offering has to be uncompromising investigative journalism but you have to get it right."
Lord Patten said that he had made no attempt to persuade Mr Entwistle to stay on.
"He went extremely honourably. I didn't try to argue him out of it because I think he had made his mind up and I think it was the right decision," he said.
"We had several conversations yesterday. He is an editor in chief of a great news organisation and I think he felt he should take responsibility for the awful journalism which disfigured that Newsnight programme."
Home Secretary Theresa May also said that she believed Mr Entwistle had taken the "right decision" in going.
"I think it is an issue of trust and credibility and building trust and credibility," she told The Andrew Marr Show.
"It's a renowned national institution but it also has a worldwide ground as well. I think the issue which is at the core of the Newsnight piece on North Wales was a question about quality of journalism and of course goes to the heart of what the BBC is about."
Lord Patten defended presenter John Humphrys whose ferocious interview with Mr Entwistle on Saturday morning's Radio 4 Today programme was widely seen to have undermined his position.
"You don't go on an interview with John Humphrys and expect the bowling to be slow full tosses," he said.
"Throughout this the BBC, in the way we have covered ourselves, has held onto the fact that above all we are a news organisation and our credibility depends on telling on the truth about ourselves and about others, however horrible it may be."
He said that he still believed that Mr Entwistle - who lasted just 54 days in the job - had been the right choice for the post.
"One of the tragedies is that he wanted to do all the right things in terms of the management of the BBC. What undermined him were exactly those failings that he wanted to address," he said.
"He is a very, very good man, cerebral, decent, honourable, brave and I am afraid that this would have overwhelmed a lot of people with those sort of skills."
Lord Patten disclosed that unlike Mr Entwistle - who said that he had not known in advance about the Newsnight programme - that he had been aware of what was going on.
He said that he had been informed of a tweet from the Bureau of Investigative Journalism, which worked on the report, suggesting it was about to expose a senior political figure as a child abuser.
"I did subsequently ask whether the programme was being properly edited, whether it was being properly managed, and I was assured that it was," he said.
He said that the BBC now needed "a thorough, radical structural overhaul".
Profile: Tim Davie, acting DG of the BBC
The man who has had the unenviable task of leading the BBC through one of the worst crises in its history thrust upon him has a rather different CV to his predecessor - one which may help him in his sudden new role.
Tim Davie, the director of BBC Audio and Music who was due to take over as the new chief executive of BBC Worldwide next month, was appointed temporary acting director of the entire organisation last night following George Entwistle's unscheduled departure.
While Mr Entwistle spent almost his entire career at the BBC, Mr Davie has no background as a journalist, producer or broadcaster.
But it is his previous career - as a brand manager and marketing executive - that may well be the BBC's saviour in the short term and the reason behind his appointment.
Mr Davie began his career in the private sector. After reading English at Cambridge University, he joined Procter and Gamble's marketing department, becoming a brand manager in 1991.
He joined the BBC from his post as marketing and franchise vice-president for PepsiCo Europe, and from April 2005 was director of the BBC's marketing, communications and audiences division.
He became head of audio and music in September 2008, with overall responsibility for BBC Radios 1, 2, 3, 4, and the BBC digital radio stations 1Xtra, 6Music, 4Extra, and the Asian Network.
Mr Davie also oversaw the three BBC orchestras in England, the BBC Singers, and the BBC Proms, as well as classical music and performance television, factual radio and radio drama production.
No stranger to controversy at the BBC, he had to address prank calls made by Jonathan Ross and Russell Brand on Radio 2, and the decision to close 6Music, which was later reversed, was made under his leadership.
Married with three young sons, Mr Davie is a member of the BBC's Executive Board, a trustee of BBC Children in Need, and board member of Radio Joint Audience Research - Rajar - the official body in charge of measuring radio audiences in the UK.
Now, while the BBC's governing body, the BBC Trust, begins the process of agreeing on a permanent successor, he will have to bring his considerable experience to bear in steering the corporation's listing ship to calmer waters.