The 18-year-old singer was axed from the competition yesterday amid rumours that he had bragged about taking cocaine.
"Gary is the mentor, the man Frankie trusted," Brookstein wrote on his Searching for Cheese blog. "I believe Frankie was told to just be himself and maybe a little be more.
"What he didn't have in voice Gary wanted him to make up in rock star bad behaviour."
He added: "Either Frankie did as he was told and acted out the life of a rock and roll star or he totally ignored Gary's orders to behave and concentrate on the competition.
"If Frankie ignored Gary what does that say about him as 'head judge'? He chooses bad songs, can't control his act, picks bad acts and lies for them?
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"If Frankie was just following orders then it was a huge error by his mentor that got him kicked out. Gary's judgement has not even been questioned."
Brookstein said: "I think Frankie was just being Frankie but egged on by the production team to be a rock star. I think it's a tragic manipulation of a young man by the X Factor which they are responsible for."
The X Factor series one winner had previously claimed that Cocozza was axed because he was "damaging the brand" and that there was "a real danger he was going to make the final".
Barlow has said that he was "hugely disappointed" Cocozza had "thrown away an opportunity like this" with his behaviour and added that he hopes he "picks himself up and somehow tries to turn this into a positive".
Show boss Simon Cowell was quoted as saying Cocozza's exit was "very sad" but added that "he has no-one to blame but himself".
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Watch Digital Spy's interview with Frankie and the X Factor Boys below:
See pictures of Frankie Cocozza on The X Factor below: