In another twist to the yearlong racism case, Cole could face FA disciplinary action less than two weeks before he is expected to make his 100th England appearance.
Terry, Cole's teammate for England and Chelsea, was banned for four matches by the FA for racially abusing Queens Park Rangers defender Anton Ferdinand. The FA judgment released Friday said Terry was found guilty of misconduct in part due to "inconsistencies" in Cole's evidence.
A response posted on Cole's Twitter account said: "Hahahahaa, well done (hash)fa I lied did I." He then added another hashtag followed by a vulgar expression.
Cole later apologized and deleted the tweet, but only after it had been retweeted about 20,000 times.
"I was really upset and tweeted my feelings in the heat of the moment," Cole said in a statement. "I apologize 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," Chelsea manager Roberto Di Matteo said. "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 QPR player denying saying. Terry was cleared of the criminal charges.
But the FA commission, which found Terry guilty, said in its written judgment released a week after the verdict 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."
It said there is "considerable doubt as to whether the request to amend paragraph 4 of Mr. Cole's statement, to include the word 'black,' was based on Mr. Cole's own personal recollections, or as a result of discussions that he had had with Mr. Barnard."
Cole's "issues and inconsistencies" were cited by the FA as helping to show "there is plainly more than enough cumulative evidence, both existing and new, to amount to a 'clear and convincing' case."
Chelsea, though, said it did not accept the criticism of Cole or Barnard.
"Ashley co-operated at all times with the FA and stands by the evidence that he gave and does not accept the criticism that has been made," the European champions said in a statement.
Rob Harris can be reached at http://twitter.com/RobHarris