The judges were asked about Gamu Nhengu's controversial departure at Judges' Houses on the spinoff show's Q&A session this evening.
Sticking up for Cole, Cowell claimed that tonight's performances from Katie Waissel, Rebecca Ferguson, Treyc Cohen and Cher Lloyd justified not picking Nhengu for the Top 16.
"It's interesting. When you sit in the Judges' Houses, you think that you have made the right decision. Then you see the tape edit and the crying and upset and you feel different," he said.
"But looking who was put through and how they performed tonight, I would have made the right decision. Music is always objective, some people like it, some not."
Cole also revealed that her decision was based on performances which were not shown on the ITV1 show. "As Simon says, that’s an edited version. The acts sing two songs. We hear from them twice and spend a week with them.
"On my gut instinct and help from my co-judge, those were the three that I thought were the best."
She added: "I love Gamu too. I would have liked to take all eight acts through [to the live shows] if I could."
Cowell also explained that the show will be doing all it can to assist Nhengu with any visa problems she is having. "We are all friends and we will do whatever we can to help her. Of course we will," he said.