Terry has apologised for the language he used after announcing he will not challenge the ban and fine of £220,000 issued by an independent Football Association regulatory commission two weeks ago.
Terry has not, however, apologised directly to Ferdinand.
The statement said: "Chelsea Football Club believes John Terry has made the correct decision by not appealing against the FA judgment relating to language he used at the QPR match last October.
"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."
The FA suspension means Terry will miss Chelsea's games against Tottenham, Manchester United - both in the Premier League and Capital One Cup - and Swansea.
Chelsea added: "Chelsea enjoys support all over the world. We have players and supporters from many different countries and cultures and our club is committed to eradicating all forms of discriminatory behaviour. John is fully committed to continue supporting that ongoing work."
Terry was found guilty by the FA commission of calling Ferdinand a "f****** black c***" during a Premier League match between Chelsea and QPR on Oct 23 last year.
He had earlier been cleared in magistrates court of a racially-motivated public order offence.
In a statement released via his representatives Elite Management, Terry said: "After careful consideration, I have decided not to appeal against the FA judgment.
"I want to take this opportunity to apologise to everyone for the language I used in the game against Queens Park Rangers last October.
"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."
Terry's statement continued: "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.
"Looking forward, 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 had ruled 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, and labelled his defence "improbable, implausible and contrived".
The commission also questioned why Terry's team-mate Ashley Cole had changed his statement to give more support to Terry's story, sparking a furious response from the Chelsea and England defender who described the FA as a "bunch of t***s" in a tweet sent on Oct 5.
Cole issued a full apology later that day and has since admitted a misconduct charge.