The 31-year-old critiqued Jay's performance of Adele's Skyfall, telling him he needed to work the stage more.
She said: "The production saved you tonight. If you're gong to sing a song by Adele, you need more suave and passion in your performance. I didn't feel that at all. Sorry."
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Simon, 55, quickly retorted: "Just to remind you, sweetie, it's a singing not an acting competition."
But Simon's reply seemed to fire Cheryl up, with her hitting back: "Fine, butdon't you ever criticise any of my acts in the future! Now, talk to your act."
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Taking to Instagram after the show, Cheryl defended her temper. She posted a picture of Simon pretending to grab her by the neck, writing: "Yes… Was one of those nights you can't tell other judges acts they didn't perform a song as well as they could or should have then when somebody remotely has an opinion on Simons act he responds with 'it's not an acting completion' [sic].
"Don't give it if you can't take it! Right [sic]."
An embarrassed-looking Dermot O'Leary apologised for the judge's behaviour, telling Jay: "I'm sorry you had to watch them argue like that.
"It's like watching my mum and dad argue."