The 50-year-old actor said he never dreamt of winning and does not know what to do with the trophy, reported Contactmusic.
"I don't know where I'm going to put it. I never thought I'd take one home, so I haven't thought that far in advance," he said.
Pitt, who made a small appearance in the film, also praised his colleague and film's lead actor Chiwetel Ejiofor.
"I think the truth is we wouldn't have been able to make this film without Brad Pitt, because of what he brings. He's a movie star. He's a huge figure in this profession, in this industry.