"Somewhere during the evening I started thinking, 'You better think of something just in case,'" Washington said. "It was a shock, it really was a shock."
The 62-year-old actor won for his role in "Fences," which he also directed. He said while it felt good to win, his goal has shifted over the years to lifting up others.
"I've won every award you can win," Washington told "GMA." "At this part of my life I'm here to support others and see them do well. That's why the most important thing to me was the case -- taking care of the other actors."
Washington said that turning 60 made him realize, "This isn't dress rehearsal, this is life," and he wants to make everything count.
"You're never going to see a U-Haul behind a hearse," Washington told "GMA." "You can't take it with you ... So what are you going to do with what you have?"
He said he focuses now on being a positive influence on the world and the people around him.
"There's so much division in the air right now," he said. "To be some kind of a force for unification, for unity, that's what I'm all about."