- Video report by ITV News correspondent Libby Wiener
The former prime minister said he was "desperately worried" about what will happen next as he admitted he thinks about the consequences of the 2016 vote "every single day".
In an interview with The Times, Mr Cameron - who called the referendum - criticised Mr Johnson's decision to take the whip from Conservative MPs and to prorogue Parliament.
Breaking his silence on his decision to hold a referendum on Britain's relationship with Europe in which he campaigned for Remain, he said it was "painful" to watch the fallout from the Brexit vote.
"I think about this every day. Every single day I think about it, the referendum and the fact that we lost and the consequences and the things that could have been done differently, and I worry desperately about what is going to happen next," he told the paper.
"I think we can get to a situation where we leave but we are friends, neighbours and partners. We can get there, but I would love to fast-forward to that moment because it's painful for the country and it's painful to watch."
Several of his Tory colleagues, including Mr Johnson, Mr Gove and the home secretary Priti Patel, formed part of the Leave side which saw Conservatives "go against each" in a way Mr Cameron said he had not thought they could.
He told The Times: "I say in the book: Boris had never argued for leaving the EU, right? Michael was a very strong Eurosceptic, but someone whom I'd known as this liberal, compassionate, rational Conservative ended up making arguments about Turkey (joining) and being swamped and what have you.
"They were trashing the government of which they were a part, effectively."
Mr Cameron told the paper he thought a second referendum could not be ruled out "because we're stuck."
"I'm not saying one will happen or should happen. I'm just saying that you can't rule things out right now because you've got to find some way of unblocking the blockage," he said in response to whether a second vote should be called.
"I think there are certain things you shouldn't do to unblock the blockage. I think proroguing parliament - pretending it doesn't exist - I think that would be a bad thing."
Mr Cameron said a no-deal Brexit would be a "bad outcome" for the country, adding: "I very much hope it doesn't happen. I don't think it should be pursued."
Despite his differences with Mr Johnson, the former MP for Witney said the current prime minister was "easy to work with".
"I want him to succeed. I worked with him well, as I say in the book. I also say that he was a capable mayor. He was easy to work with. I thought he was very talented. I wanted him in my government."
But Mr Cameron was less positive about Mr Johnson's first 50 days in office.
He said: "Of course, as a new prime minister, I wished Boris well. I wanted him to get a deal from the EU that would have passed in the House of Commons.
"If that was to happen, I would have been elated. But clearly, while he started out down that road, the strategy has morphed into something quite different.
"Taking the whip from hard-working Conservative MPs and sharp practices using prorogation of Parliament have rebounded. I didn't support either of those things. Neither do I think a no-deal Brexit is a good idea."
Earlier, Mr Johnson said he held his former colleague with "affection and respect".
"I think he has a very distinguished record and a legacy to be proud of," he added.
- David Cameron's first in depth television interview about his time in office will be broadcast on ITV on Monday 16th September at 8pm