Last month, an independent panel ruled that Terry had directed racist language at Ferdinand in the Premier League match, and the Chelsea captain was given two weeks to issue a response to the verdict.
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"Although I'm disappointed with the FA judgment, I accept that the language I used, regardless of the context, is not acceptable on the football field or indeed in any walk of life.
"As I stated in the criminal case, with the benefit of hindsight my language was clearly not an appropriate reaction to the situation for someone in my position.
"My response was below the level expected by Chelsea Football Club, and by me, and it will not happen again.
"I will continue to do my part in assisting the club to remove all types of discriminatory behaviour from football.
"I am extremely grateful for the consistent support of Chelsea FC, the fans and my family."
The three-man panel judging Terry's case concluded that he was not a racist, but were not satisfied by his defence, describing it as "improbable, implausible and contrived".
Earlier in the year the Chelsea defender was cleared by Westminster Magistrates' Court of racially abusing Ferdinand.
He will now miss the club's Premier League and League Cup matches with Manchester United, as well as Saturday's clash with Tottenham and a game with Swansea City.