After being announced as safe during the results show, Frankie had exclaimed: "F**King have it. Get in there."
Today Channel TV, who are responsible for ITV's compliance with the Ofcom broadcasting code, apologised for causing any offense.
They said that it deeply regretted Frankie Cocozza’s “unexpected and unprompted outburst” and had already apologised directly to viewers who had contacted ITV to complain.
Bosses claimed that they did not hear Frankie's words above noise in and around the studio at the time of the broadcast, and only became aware of the incident during The Xtra Factor on ITV2 some 45 minutes later.
Criticising the channel, Ofcom branded the Frankie's use of language "particularly unacceptable" due to the family audience that The X Factor attracts.
Finding the show in breach of its broadcasting code, Ofcom revealed it was "particularly concerned" that the show's team were not aware of the problem sooner.
They added in a statement: "Had there been suitable compliance procedures in place the broadcaster could have responded in a more timely and appropriate fashion."
In a separate investigation, Ofcom dismissed complaints over footage of Frankie's drinking and smoking shown during the show.