The Chelsea captain and his advisers had two weeks to study the full written reasons of the decision by an FA independent regulatory commission.
Terry, who was also fined £220,000, has apologised after the panel labelled his defence "improbable, implausible and contrived".
"I want to take this opportunity to apologise to everyone for the language I used in the game," Terry said.
"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."
It means he will miss Saturday's game with Tottenham as well as the clash with Manchester United on October 28 and then the Carling Cup clash between the two sides three days later. Chelsea's trip to Swansea will be the final game he will be absent for.
Chelsea released a statement saying they approved of Terry's decision not to appeal, and revealed they would take disciplinary action against their captain - the nature of which would remain confidential.
Ther club said: "Chelsea also appreciates, and supports, John's full apology for the language he used. The club firmly believes such language is not acceptable and fell below the standards expected of John as a Chelsea player.
"The Board has conducted its own investigation into the matter, and considered the various issues involved. The Board has taken further disciplinary action in addition to the four-match suspension and £220,000 fine imposed by the FA. In accordance with our long-standing policy, that disciplinary action will remain confidential."
Terry's statement concluded: "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."
Terry was accused of calling Ferdinand a "f****** black c***" in the 83rd minute of Chelsea's defeat at Loftus Road last October.
The panel said the Chelsea captain, 31, "is not a racist" but were "satisfied" his comments were used as an insult.
The three-man panel said there was "no credible basis" for Terry's claim he had only been repeating words he thought QPR defender Ferdinand had accused him of saying.
MATCHES TERRY WILL MISS
Tottenham v Chelsea - Premier League, 6 Oct
Chelsea v Manchester United - Premier League, 28 Oct
Chelsea v Manchester United - Capital One Cup, 31 Oct
Swansea v Chelsea - Premier League, 3 Nov
- Chelsea Football Club
- Manchester United