The Blues defender launched a foul-mouthed tirade on the social networking website in response to the governing body's report on John Terry's recent racism case
Earlier on Friday the England left-back had tweeted: "Hahahahaa, well done #fa I lied did I, #BUNCHOFT****" before deleting the Tweet.
He was responding to the publication of the FA report revealing the reasons behind the guilty verdict handed down to John Terry over the racial abuse of Anton Ferdinand.
However, the 31-year-old has now released an official statement, showing remorse for his tirade at the governing body.
In a statement, Cole said: "I was really upset and tweeted my feelings in the heat of the moment. I apologise unreservedly for my comment about the FA."