The Chelsea left back apologized in person to FA chairman David Bernstein for posting a vulgar tweet after a commission set up by the governing body questioned the evidence Cole gave in defending John Terry in a racism case.
"He expressed a degree of remorse for what he had done, wished it hadn't happened," Bernstein said. "I looked him in the eye and really felt that he meant it."
Cole has been charged with misconduct by the FA and is set to be fined, but is free to play for England in Friday's match against San Marino and the away game in Poland on Tuesday - if selected by coach Roy Hodgson.
"His contrition is greater because he realizes that he might have put his position in jeopardy - and I'm very happy he hasn't done that," Hodgson said.
Cole is currently training with the England squad at the country's new national training center in Burton-upon-Trent, where he greeted Prince William and his wife, Kate, at the facility's official opening. William is the honorary president of the FA, which Cole criticized in the vulgar tweet on Friday.
Cole has made 98 appearances and will become only the sixth Englishman to reach the century mark if he plays against San Marino and Poland. He is unlikely to be made captain to mark the occasion, however.
"We've had issues and we've stated publicly many times that we have a very high level of behavior and so on and so forth required from an English captain," Bernstein said.
Cole has until Thursday to respond to the FA charge. He had already issued an apology through his lawyers soon after sending the tweet in question.
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