"I'm personally loathe to acknowledge the kind of wonderful response this film has received for fear of becoming addicted to it, so suffice it to say, it's been really nice," Fincher told the AP.
Other wins for the film went to Trent Reznor and Atticus Ross for best music and to Aaron Sorkin for best screenplay.
"Mark Zuckerberg, if you're watching, Rooney Mara makes a prediction at the beginning of the movie. She was wrong. You turned out to be a great entrepreneur, a great visionary and an incredible altruist," Sorkin said.
The film follows Facebook founder Mark Zuckerberg's life as he created the now, hugely poplar social website.