However, O'Shaughnessy will compete in the Britain's Got Talent semi-finals, despite Cowell's displeasure at the conflict.
"I'm over the moon to be through to the semi-finals," O'Shaughnessy told ITV's Britain's Got Talent site. "I was contracted to do another show, but I've since been released from my contract.
'I want to thank the judges for giving me a second chance. The reveal was such an emotional ordeal for me. I was fraught with nerves. I felt as though I'd let Simon down. Simon's somebody you want to please, so it felt awful to disappoint him.
'I'm looking forward to the live shows. I've been working on new material and focusing on the music."
The Britain's Got Talent semi-finals begin tomorrow (May 6) and run through until Thursday (May 10).
Watch Ryan O'Shaughnessy performing 'No Name' below: