Speaking to The Telegraph, the former Brexit secretary claimed he “felt the need to give the Prime Minister a nudge”.
He said: "What he essentially said was 'it's not my fault', undermining his apology from last week. ‘Nobody told me what my rules were?’ It sounds pompous.
“But there's a moral requirement of leadership. If you make a mistake, you've got to accept the blame, not try to blame somebody else.
"I don't know why he did that interview. It wasn't really a mea culpa – it was somebody else's culpa. If he really meant 'let's wait for the outcome of the Sue Gray inquiry', why was he out giving interviews?
"I've just made myself the most unpopular person in the Tory party.
"Well, the second-most unpopular. But I've gone from thinking maybe we can rescue it to maybe we just have to accelerate it and get it done.”
It follows Mr Johnson's 14-minute TV interview on Tuesday, in which he insisted "nobody told me" that a gathering in the Downing Street garden during the May 2020 lockdown was against the rules.
Mr Davis warned failing to act now was simply dragging out the inevitable.
He explained: "The party is going to have to make a decision or we face dying a death of 1,000 cuts.
"We'll have Sue Gray, and he [Mr Johnson] will have to fire some people and that's going to look like shifting the blame, so that won't go down well. Then we'll have to go through people being hit by higher energy bills and then having to pay more in National Insurance.
"Those are going to be crises in their own right – and then there will be other crises because of the disorganisation at No. 10.
" And every single time we have a crisis, you will get one or two more letters going in, and we could end up with a confidence vote at Christmas of this year which means we will have had a year of agony.
"That's the worst outcome, particularly for the 2019 and 2017 and 2015 intake – that, slice by slice by slice, this carries on and we bump along at minus whatever and, even worse, we create policies to try to paper over it."
On Wednesday, Mr Davis had told the Prime Minister he had spent weeks defending him from “angry constituents”, including by reminding them of the “successes of Brexit”.
Mr Davis said: “I expect my leaders to shoulder the responsibility for the actions they take.
"Yesterday, he did the opposite of that, so I will remind him of a quotation which may be familiar to his ear: Leopold Amery to Neville Chamberlain.
“You have sat too long here for any good you have been doing. In the name of God, go.”