The judge's criticism of Davis's performance in the final prompted the youngster to become tearful on the live ITV1 show.
Speaking to GMTV, Cowell, 49, admitted that he was wrong to treat him like an adult and upset him on "the most important night of his life".
"The time that I felt really bad, I have to be honest with you, is when I made Aidan cry on the final," he said. "That's when I thought I went too far.
"It's a very difficult situation when you're like, 'Do I treat you like adult, do I treat you as a kid? What's the right thing to do?' And I made the wrong call because actually it was the most important night of his life and I upset him.
"I've got to tell you, that really, really hurt me because I hurt him, and I felt terrible."
However, Cowell defended his decision to allow ten-year-old Holly Steel a second chance to perform on the show after she burst into tears during her first rendition of 'Edelweiss'.
"It was tough with Holly," he said. "You know, you've done live TV all your life. And in the middle of a live show, that happens - you just don't know what to do. What's the right thing or the wrong thing?
"Ironically I got more complaints about that than anything else. When people were saying about Ofcom getting complaints, all the complaints really were about the fact that I had given her a second chance.
"But again I would do that - if I had the chance - I would do it again. It felt like the right thing to do."