The 'What Makes You Beautiful' stars have become the first UK band to go straight to the US album chart number one spot with a debut record.
Speaking on the phone on Daybreak, Payne said: "It still seems strange to say that, everything's happened this quickly. We didn't expect to be over here releasing an album. I don't think it's quite hit home yet."
Payne explained that he and his bandmates were "lucky" to be in their position after they were put together by Simon Cowell in The X Factor after failed solo auditions.
"It's just really surreal to think you were one of those five lucky people," he said. "Anyone could have been chosen that day."
He added that the group were "naive" about what their US success means within the music industry.
"We're all still naive to the music industry. People tell you all these stats and tell you that you're great, but you kind of just smile, because you don't really understand it that much, so you just go with it, I suppose."
Up All Night shifted 176,000 copies in its first week on sale, Nielsen SoundScan figures suggest.
One Direction will appear on Saturday Night Live on April 7.
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Watch the music video for 'What Makes You Beautiful' by One Direction below: