The England international sparked controversy when he labelled the English governing body a "bunch of twats" via social network site Twitter.
The 63-page document stated that Cole, who appeared as a character witness for Terry in his criminal trial in July, had not originally included the word "black", having the effect of "bolstering Mr Terry's claim that the words that he spoke to Mr Ferdinand were not said by way of an insult, but as repetition and forceful denial of what Mr Ferdinand had accused him of saying".
The report has claimed that Chelsea had encouraged Cole to change his statement and add the word, which prompted the left-back to accuse the governing body of branding him a liar.
Cole, who released a statement via his solicitors, said: "I had just finished training and saw the captions on the TV screens in the treatment rooms about what was said in the FA Commission ruling about me.
"I was really upset and tweeted my feelings in the heat of the moment. I apologise unreservedly for my comment about the FA."
Meanwhile, Terry has two weeks to decide on whether to appeal the four-match ban.