The 18-year-old, who was kicked out of the show on Tuesday for breaking the rules, confessed he has taken cocaine six times in his life.
In an interview with the Sun, the party-loving teenager also revealed he has slept with seven girls since he became a contestant.
Cocozza told the newspaper: “All I can say is I will regret this for the rest of my life. I was an idiot and it was just a stupid thing to do.”
He added: “I feel bad about letting the fans down and I’d like to apologise to the people who voted for me. I’m really, really sorry.”
Cocozza also apologised to his mentor Gary Barlow and the staff of the ITV1 show. Show chiefs axed the teenager after he was heard bragging about drugs, which programme bosses said broke the rules.
In the interview, the mop-haired youngster said he first tried cocaine as a 16-year-old school leaver.
He said: “I’ve never bought coke myself but I’ve done it about six times when I’ve been pissed and it has been offered to me.”
Cocozza also confessed to trying illegal high mephedrone in the past, and admitted he had “smoked a lot of weed”. He said he went off the rails after Saturday’s show as he was criticised in front of millions following a below-par performance.
“I was embarrassed and totally devastated by what they said about me, so I went mental – a bit too mental,” he told the newspaper.
He said he drank “loads” at a party and took one line of cocaine – the first time he had taken the drug since of June. But he denied being high on Sunday night’s results show.
Judge Barlow has since said he felt a “level of responsibility” for Cocozza’s departure.