Cole, who was a judge on the ITV1 show from 2008 to 2010, admitted in the book that she wasn't convinced about Waissel's talent after her first audition.
She eventually took Waissel to live shows as her mentor because she was "quirky" and boss Simon Cowell had previously advised her about what made "good TV".
"Simon had spent the past two years drumming into me that we needed acts who would be 'good TV'," Cole confessed in her autobiography.
"When I saw Katie perform... I had to admit that she was... quirky, intriguing and busting to succeed.
"In short, she had the character and drive it took to withstand the pressure of the show, and so I put her through, even though she messed up when she sang in front of Will (will.i.am)."
After reading the comments, Waissel tweeted: "@cherylcole thought you were better than this. Shame I trusted you. you live and you learn."
Cole, who is currently working on Girls Aloud's comeback, is yet to respond to Waissel.