The ex-Tory leader denied the move to hold the vote was all about politics, insisting he hoped it would “fix” Britain’s position within the EU.
He told CNN: “I don’t regret holding a referendum. I think it was the right thing to do.
“I don’t think you can belong to these organisations and see their powers grow, and treaty after treaty, and power after power going from Westminster to Brussels and never asking the people whether they are happy governed in that way.
“But, I haven’t changed my mind about the result of the referendum. I wish the vote had gone another way.
“I think we have taken the wrong course.”
Asked if he was worried his legacy would be defined by his decision to call the Brexit referendum, Mr Cameron said: “I think people will make up their own minds.
“I, obviously, believe that I was right to hold a referendum. I made a promise to the British people. I kept that promise.
“The point I would make is that people say this was all about politics, and, of course, there is always politics involved in these decisions, but there was also, I believe, a quite fundamental problem that Britain had, and Britain was seeing, with the development of the single currency, the beginning of decisions being made about us without us, and we needed to fix our position.
“I wanted to fix it inside the European Union. The British public chose that we would fix it from outside the European Union.
“And, I wish my successor well with her work in being, what I hope will be a good, and friendly, and close neighbour to the European Union.
“Rather than as we were, perhaps we were, a slightly reluctant and sometimes unhappy tenant.”
Mr Cameron added: “But, to be frank, Britain is the fifth, or sixth, largest economy in the world. It is a legitimate choice to try and be a friend and a neighbour, and a partner of the European Union, rather than a member of the European Union.
“And that’s what the country has chosen. I accept the result. I wish my successor well in the work that she is doing.
“I know as being prime minister, it is a hard enough job without your predecessor giving you a running commentary, and that’s why I haven’t been giving interviews, and the rest of it.”
Mr Cameron offered Prime Minister Theresa May strong support on her decision to strike Syria after the Commons blocked his attempt to take action in 2013.
“I deeply regret that Parliament didn’t vote for similar action in 2013,” he said.
“I think she has done the right thing. This is not about regime change in Syria, although, God knows we need it.
“It’s not about intervening in the civil war. It is about making a point that the use of chemical weapons is unacceptable.”