Cowell told People magazine before Friday's Season 9 auditions in Denver that Abdul would not be returning to the popular Fox singing competition following a contract dispute with "Idol" producers.
"I'm going to miss her. She's my buddy," Cowell said.
"Paula has been very cool about the whole thing. And let me tell you, Paula is going to be fine."
On hand to judge the second round of auditions in Denver were Cowell, Kara DioGuardi and Randy Jackson. Singer Victoria Beckham served as a guest judge in lieu of Abdul.
"I'm very sad. I talked to her last week," DioGuardi said of Abdul's absence. "It's sad, but it was her choice."
"I talked to (Paula) a couple days ago and she's going to be great," Jackson offered of the former "Idol" judge.