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The star was nominated for his performance in Invictus, but the gong instead went to Christoph Waltz for his turn in Inglourious Basterds.
When asked if he was okay with losing out on the award, Damon told Metro: "Of course. Clearly I wasn't going to win!
"I'm a huge fan of everyone in my category but, with respect to all of them, we knew Mr Waltz had taken the pressure off the rest of us. There were no speeches in any of our pockets."
Prior to the Oscars ceremony, Damon quipped that he had challenged fellow nominee Stanley Tucci to see who could "look more magnanimous when Christoph Waltz wins".
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