The pair were rumoured to be dating before the start of this year's live shows, but Cocozza told Heat that the reports were inaccurate.
"Amelia and me was blown way out of proportion," Cocozza said. "We were more mates than anything and had a laugh in the house."
He denied having sex with the 17-year-old and added: "Amelia and I were just friends. We were very close, but just as friends. We didn't snog."
Cocozza was axed from the show earlier this month after being overheard talking about taking cocaine.
Lily was voted off the show by her mentor Kelly Rowland in the first-week twist, but was reintroduced following Cocozza's exit and survived this weekend's sing-off, which went to deadlock.
Speaking after her first elimination, Lily told Digital Spy that the press "love to make up stories" and laughed off reports that she and Cocozza were an item.
> X Factor Frankie Cocozza 'caught taking cocaine in nightclub'
>The Wanted: 'We'd give Frankie Cocozza a record deal'
Cocozza's father Frankie Snr later claimed that his son had "a kiss and a cuddle" with Lily following her initial exit, while she was reported to have comforted Cocozza following his week two sing-off victory.
Lily later said that Cocozza's exit from the show was "bittersweet", as it gave her the opportunity to return to the contest.
In his latest interview, Cocozza revealed that he has slept with 71 women since losing his virginity at the age of 12. He added that he has had sex with seven women since the first X Factor live show.