The independent Football Association regulatory commission said there were discrepancies in Cole's initial statement to FA interviewers of what he heard Anton Ferdinand say to Terry compared to a later statement.
Cole responded on his official Twitter account on Friday afternoon: "Hahahahaa, well done #fa I lied did I, #BUNCHOFT****".
The Chelsea and England full-back's evidence proved crucial to Terry in his acquittal at Westminster Magistrates Court in July, but the FA commission last week banned Terry for four matches for racially abusing Ferdinand.
Asked about Cole's tweet, Chelsea manager Roberto Di Matteo said they would look into it.
Di Matteo said: "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's involvement surrounded Terry's claim that he had only been repeating the words "f***ing black c***" that he thought Ferdinand had accused him of saying. Cole backed up his team-mate and said he thought Ferdinand may have used the word 'black' during a verbal exchange with Terry.
But according to the FA commission's written reasons published on Friday morning, Cole did not mention the word 'black' in the initial interview with the FA on October 28.
On November 3, Chelsea club secretary David Barnard asked the FA for the specific word 'black' to be inserted into Cole's witness statement, suggesting that Cole may have heard Ferdinand use the term.
The commission saw an email exchange between the FA and Barnard and said that should be regarded as "cogent new evidence".
Source: PA
Source: PA