(CBS) Daniel Day Lewis admits winning his second Oscar humbles him.

"It would be a shame not to be, wouldn't it?" he remarked to Early Show co-anchor Harry Smith after taking home Best Actor honors for playing a ruthless oil pioneer in "There Will Be Blood."

They chatted at the Governors Ball, after the 80th annual Academy Awards presentation."

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80th Annual Academy Awards Winners List

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""I come from a country that has all kinds of fairly ancient traditions," Day-Lewis, who is British, continued, "but this is a tradition I am very proud to be part of. I really am."

Until Sunday night, Tilda Swinton was best-known for playing the white witch in "The Cronicles of Narnia." Now, Swinton is an Academy Award winner for her supporting role in "Michael Clayton."

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Photos: Oscar Red Carpet

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"I was beyond surprised," she told Smith. "I was ... waiting for somebody else to get up, and then this sort of wave of sand came on me and I recognized my own name, and I realized the worst had happened, and I was gonna hafta stand up in front of a billion people and make a fool of myself!"

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Photos: Oscar Moments

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"Swinton kidded in accepting her statue during the show that her agent looks just like Oscar, and she pointed the agent out to Smith afterwards, adding that she is going to give the statuette to him and keep the envelope with her name in it "as proof" that she won.

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Photos: Oscar Sees Red

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But, Smith says, Oscars host Jon Stewart may have been the night's biggest winner, who got strong reviews even though the telecast was put together in just two weeks, dkue to the writers' strike.

"We really enjoyed it," Stewart told Smith. "I think maybe having the schedule so compact kinda just forced us to focus, instead of what we normally do, which is -- play video games 'til three in the morning! So I think we were locked in."

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