"It's unbelievable," Bridges, 60, told PEOPLE at the Governor's Ball after winning the Best Actor Oscar on Sunday for Crazy Heart, nearly 40 years after his first nomination, for 1971's The Last Picture Show.
"This could be a dream," he said. "I might wake up. Maybe not. Not for a while, anyway."
The actor credited his friends, family and colleagues for their love and support during his long and winding road through Hollywood. During his acceptance speech, he raised the Oscar to the sky and addressed his late parents, Lloyd and Dorothy.
"Thank you, Mom and Dad, for turning me on to such a groovy profession," he said. "This is honoring them as much as it is me."
Asked later by PEOPLE what the Oscar means to him, he replied: "Sharing this with all the people who mean the most to me, my director and all my cast members and other actors and directors I've worked with that I haven't seen in years. I saw Walter Mirisch, who gave me my first job [in 1970's Halls of Anger], so that was kind of cool."
Just as he did on stage, Bridges told PEOPLE that his wife Susan deserves the most credit of all, for being there every day for the past 33 years – no matter what transformations his movie roles call for.
Asked about his current beard, Bridges said, "I let all my growths on my body grow between parts, and then I shape them for the [next] part. Susan takes me however I am – hairless, a lot of hair. I've had hair longer than you, and she loved me like that. I've had no hair, she loved me then."