The teenage singer was axed from the competition on Tuesday (November 8) after breaking an X Factor golden rule, allegedly by bragging about using cocaine to members of the production team.
In an interview to be screened on tonight's (Saturday's) Xtra Factor, Cocozza again apologised for his actions and accepted that he should have changed his behaviour as viewers began regarding him as a role model.
"I didn't even think [about being a role model] at all," he confessed.
"Then all of a sudden there's people saying, 'You need to sort yourself out, you're a role model', but from my first audition I walked out on stage and got my bum out and had seven girls tattooed on it. And people are saying, 'He's not a good role model', but they should have known that from the start.
"I've had this massive reaction, and reading all the stuff, I've realised that I was starting to be a role model and yeah I feel bad about that now, really bad about it now. Hopefully one day maybe people will look up to me in a good way. Can't really see it happening but who knows?"
Watch Gary Barlow discuss Frankie Cocozza's X Factor exit below:
Cocozza went on to say: "Gary said you need to tone it down after I'd been out a few times. Quite a few people told me to calm down really. It's been a hard few weeks.
"No-one gave a scoobie who I am, now people in the street are trying to give me a hard time. It's not easy, but I've got to deal with it myself."
He added: "I've learnt that you get out what you put in and my actions aren't just going to affect me. It's not all about me, it is going to affect my family. I've got to stop being a little s**t."
> 'X Factor's Frankie Cocozza: "I'm not an addict, I'm an idiot"
> Frankie Cocozza arrives home after 'X Factor' axe - pictures
> Jason Donovan: 'Frankie Cocozza exit has been tough on Gary Barlow'
Cocozza went on to insist that he had taken The X Factor seriously and was "gutted" to be ejected from the contest.
"There's a lot of people trying to give me a hard time, but no matter how they try they're not going to be able to give me a harder time than I'm giving myself," he said.
"I did take it seriously. I was given the most unbelievable opportunity and I'm so grateful for that. I know I will regret going out, but I'm so grateful for the opportunity I was given and I'm gutted."
During the interview, Cocozza repeatedly thanked viewers, the X Factor team and his mentor Barlow for "supporting [him] and making the journey last as long as it did", adding: "I'm sorry I let you all down."
Watch the full interview with Frankie Cocozza on The Xtra Factor tonight at 9.45pm on ITV2.
> Simon Cowell: 'X Factor Frankie Cocozza can only blame himself'
> Frankie Cocozza 'X Factor' exit is bittersweet, says Amelia Lily
> 'X Factor' Jonjo Kerr: 'Leave Frankie Cocozza alone'
Scroll through a gallery of Frankie Cocozza's time on The X Factor below: