The 'X Factor' judge - who had mentored the 18-year-old hopeful before he was kicked off the ITV1 show - explained despite being sad to see Frankie forced to leave the competition, he will always be a "friend and supporter" of the teen rocker.
In a statement released to BANG Showbiz, Gary said: "Frankie has apologised publicly as well as personally to me and the producers for his actions that lead to him leaving the show.
"I'm hugely disappointed that he's thrown away an opportunity like this after working so hard to get here. I'm sorry to see him go as we've been through a lot together in such a short time.
"I hope Frankie continues to look to me as a friend and supporter and works it all out, picks himself up and somehow tries to turn this into a positive."
The party-loving lothario - whose wild antics had been a focal point throughout his time on the show - was forced to quit 'The X Factor' after admitting he had become "out of control" in recent weeks.
Frankie said: "I'd like to apologise to Gary, my fellow contestants and everyone who has voted for me, but, as of today, I will no longer be in 'The X Factor'.
"My life during the show has gone out of control and my behaviour off stage has over-stepped the rules of the competition. I no longer deserve my place in the show, so I am therefore leaving. I would like to thank everyone who has supported me."