The Beatles drummer said he did not vote in the referendum as he was abroad at the time of the Brexit poll, but nonetheless supports withdrawal from the EU.
He told BBC Newsnight: "The people voted and they have to get on with it. Suddenly, it's like 'oh well, we don't like that vote'.
"What do you mean you don't like that vote? You've had that vote. This is what won, let's get on with it."
In a reference to arch-Remain campaigner Bob Geldof, Starr said: "I didn't vote - I was out of the country. I would've voted for Brexit.
"Yeah, I would've voted to get out. But don't tell Bob Geldof."
He added: "It's a great move. I think, you know, to be in control of your own country is a good move."