The 27-year-old beauty - who was officially replaced on the show by Nicole Scherzinger earlier this week following two weeks of speculation - is upset the music mogul had created a "circus" around the talent show and believes it is "shoddy" her dismissal was made public before there had been any official statement.
A source said: "Cheryl is very much her own person and she hated the circus that the 'X Factor' had become.
"She was annoyed that when the bad news came, Simon did not even have the guts to tell her himself and left it to another executive.
"But she was even more upset that the discussions over her contract became open season for everyone. It was shoddy to say the least."
Cheryl is also said to have hit out at 51-year-old Simon by claiming she is no one's "puppet" in text messages to her friends.
The source added to the Daily Mirror newspaper: "After the reports surfaced at the weekend that Cowell wanted her back, her pals were clamouring to know what was going on.
"Her text response was short and brutal - that she was 'no one's puppet.' It said it all. And while not mentioning Cowell by name it was clear who she meant."
Meanwhile, Nicole - who was originally supposed to co-host the show with Welsh presenter Steve Jones - has confirmed she only found out she had replaced Cheryl as a judge when she read reports in the press.
She said: "I haven't said this yet, but I think it's official that I have been made a judge. It's an amazing opportunity.
"I'm kind of finding out along with everyone else. It's kind of crazy to read about it in the newspaper first."