The former X Factor star's indie-pop track only managed to premiere at number 89, trailing behind re-entries from Des'ree, whose 'I'm Kissing You' originally charted in 1997, and No Doubt's 'Don't Speak', from 1996.
Cocozza rose to fame as part of last year's series of the singing competition, but was kicked off after he broke a 'golden rule' of the show, alleged to involve drug-taking.
He has since slammed The X Factor's producers, saying that they encouraged his bad behaviour.
"I just got caned week in, week out. I didn't want to be there but they did everything they could to keep me in," Cocozza told the Daily Star.
"Then when I kept getting through each week I think they thought: 'S**t, he could win this and we can't have that', so they f**ked me off in the most horrible way."
Watch the video to Frankie Cocozza's 'She's Got a Motorcycle' below:
Photo gallery - Top ten X Factor controversies:
Copyright: Rex Features Ken McKay/Rex Features