The outgoing Brexit Secretary said the Government had gone further than it should have in the negotiations, and warned it was a “dangerous strategy”.
His late-night resignation plunged Mrs May into a fresh leadership crisis and he was swiftly followed out of the Department for Exiting the EU by ally Steve Baker.
But Mr Davis said a leadership challenge would be the “wrong thing to do” and insisted he believed Mrs May was a “good prime minister”.
Asked if she could survive, he replied: “Oh yes, of course.”
Mr Davis told BBC Radio 4’s Today: “When we debated this at Cabinet on Friday my opening remark to Theresa was ‘Prime Minister, as you know I’m going to be the odd man out in this’.
“She knew this because I had written to her earlier in the week.”
He admitted he had “lost the argument in Cabinet”, adding: “In my view, this policy has got a number of weaknesses.
“I would be front and centre in delivering this policy, explaining it to the House, persuading the House it is right, and then going out and delivering it with the EU.
“Frankly, just as it was known what the policy was, it was also known I had concerns about it.
“It would not have been a plausible thing to do and I wouldn’t have done a good job at it.”