Exclusive Photo: See How Mark Rylance Celebrated His Oscar Win the Morning After

Mark Rylance took home the Academy Award for Best Supporting Actor for his turn in Bridge of Spies on Sunday night. And after making his rounds at the Vanity Fair Oscars party later in the evening, the actor was still beaming with joy from his big win.

So how did he celebrate the momentous occasion the next morning? By eating breakfast with his little golden man, of course.

The morning after he took home the Oscar, PEOPLE caught up with Rylance, 56, at the Beverly Wilshire, a Four Seasons Hotel, where he was the first to admit that it all "takes a while to sink in." In fact, Rylance revealed that not too long ago, he could have never imagined himself winning an Academy Award.

For much more from Mark Rylance and even more on this year's Oscars ceremony, pick up the latest issue of PEOPLE, on newsstands Friday

"A few years ago I gave up film," he said, explaining that his decision came after working on the set of a "very, very bad film."

"I remember looking for the director, who hadn't turned up at all. The director was playing on his Gameboy 200 yards away in the warehouse," he said. "I got rid of all my agents and I said, 'I don't want to be in film anymore. I'm perfectly happy being a theater actor.' "

Then Steven Spielberg offered him the role as Rudolf Abel in Bridge of Spies.

"I would work with Steven no matter what medium he did," he said. "I always wanted to be as good an actor as the actors I watched, like [Robert] De Niro and [Al] Pacino."

And it didn't hit Rylance that he had won the Oscar until he found himself doing the "Winner's Walk" surrounded by pictures of his film idols.

"They stuck all these pictures of, like, Mickey Rooney and De Niro [in the hallway]," he said. "So to be part of this, is astounding."

For his wife Claire, watching her husband accept the award was something she always believed could happen.

"I also thought it was always going to happen at some point," she told PEOPLE. "I personally think he is the best actor in the world. I was stunned by the feeling that came of the audience – the genuine joy."

• Reporting by MARY GREEN