Cocozza was caught on camera yelling "f**king have it" after he discovered that he was through to the next stage of the ITV1 talent show.
The broadcaster said that it did not make an on-air apology because it did not believe his comments were audible to viewers.
© Ken McKay/TalkbackThames/Rex Features
According to the Daily Mail, there were 20 complaints about Cocozza's swearing.
An X Factor rep said: "Emotions were running high during the live show and we apologise if any potentially offensive language was audible.
"All the contestants are reminded of their responsibilities regarding language on the live shows."
Cocozza was encouraged to embrace his wilder side by mentor Gary Barlow and producers last week and was allowed out to party in London.
The 18-year-old from Brighton found himself in the bottom two the previous week after failing to impress viewers with his cover of Coldplay's 'The Scientist'.
