The actor, who won Best Actor in a Motion Picture, Drama, for Manchester by the Sea, opened up to E! News at the Amazon after-party and gushed about his first-time win.
"It's really nice. To hear my name called was a kind of other worldly, surreal, strange experience," Casey said.
Although there was plenty of buzz surrounding his film before the Golden Globes, Casey still didn't expect to win. "This was a very different room," he added. "This was a room full of people who are very, very impressive and have been for years. They have a lot of presence and you're sitting next to them and watching them on stage, and Meryl Streep makes that speech and people are up there saying incredible things."
Essentially, the Good Will Hunting actor couldn't believe he stacked up to the other stars in the room. "They're incredible people who have been doing this forever, so it's all pretty dazzling and overwhelming," Casey continued.
Ben Affleck's brother faced some fierce competition in his category from actors such as Joel Edgerton for his role in Loving, Andrew Garfield for Hacksaw Ridge, Viggo Mortensen for Captain Fantastic and Denzel Washington for Fences.
But it was Streep's powerful speech that left Casey, well, speechless. "She's so composed and has so much poise and depth, I think I was holding my breath most of the time," he said.
Of course, Casey gave an emotional acceptance speech of his own. "There is no award that belongs to just one actor. I wish that Michelle [Williams] could be onstage with me, because she made most of it work. She's perfect...I just have to thank everyone, I know it's boring, but everyone who made the movie, otherwise it wouldn't happen," he gushed. "Thank you to everyone there and to Kevin Walsh and to Matt Damon for giving me the opportunity, your support, your friendship. I suspect you won't be passing on any more movies in the future when I might be anywhere nearby, but I'll take this one."
For complete Golden Globes coverage, watch E! News at 7 p.m. and 11 p.m.