Cole responded on his official Twitter account saying: "Hahahahaa, well done #fa I lied did I, #BUNCHOFT****"."
It was re-tweeted more than 19 thousand times before he deleted it.
In a statement released this afternoon, Cole said: "I had just finished training and saw the captions on the TV screens in the treatment rooms about what was said in the
"I was really upset and tweeted my feelings in the heat of the moment. I apologise unreservedly for my comment about the FA."
The FA has not yet commented on the tweet, but Chelsea manager Roberto di Matteo said the club would investigate: "We'll look at the tweet and then we'll see. Apart from this, I don't think the players are out of control."
Cole has backed up Terry's defence that the racial slur was only used to counter an accusation of racism he claimed Ferdinand was levelling at him.
Cole told Terry's criminal trial in July that he believed he heard Ferdinand use the word "black" during the confrontation, something the Queens Park Rangers defender denied saying.
Terry was cleared of the criminal charges but found guilty by the FA and banned for four matches.
But in its written judgment, the FA commission said that Cole did not mention the word "black" in the initial interview with them after the October match.
Later, though, Chelsea club secretary David Barnard wrote to the FA's disciplinary unit asking for the word "black" to be added into Cole's statement.
The three-man FA panel dedicated a section of its judgment to "the 'evolution' of Ashley Cole's evidence."
Cole could face FA disciplinary action less than two weeks before he is expected to make his 100th England appearance.
English Premier League
Jamie Carragher has urged Liverpool to act swiftly to sort out the future of striker Luis Suarez.