The 'Stronger' singer provided her co-written track 'Tell Me a Lie' to the British boyband for their debut album Up All Night.
She described herself as a "writer's snob" who rarely gives her own tracks to other performers.
"Giving away my songs is not something I do lightly," she told the Daily Star.
"I'm very particular about that because my songs are like my babies. If I wanted it done I can sing it myself. I'm such a writer's snob.
"People have asked for songs and I'm like, 'I can't stand their voice, they're not singing my song'."
She explained that on this occasion Simon Cowell asked her if the group could use one of her songs, and she realised the track would work after hearing the band perform.
"When Simon Cowell put me forward to write for One Direction I said, 'Let me hear them first'. Simon has been really supportive since I won American Idol.
"'Tell Me a Lie' is the cut I've got on 1D's album as I like the story of them, how they came together as a group. While I wrote the song for me, it didn't fit in the current album as I never want an album to sound like one thought.
"One Direction have worked so well in America as well as the UK because people love a story, plus they have this innocence about them that attracts people."
On British success in the US, she added: "There's a lot of British talent doing well in America right now. I'm a huge fan of Ellie Goulding and Jessie J."
Kelly Clarkson recently revealed that she has already started work on the follow-up to 2011's Stronger.