Terry was banned for four matches, starting with Saturday's London derby at Tottenham, and fined £220,000 by an independent Football Association panel.
The former England defender has accepted the sanction and issued an apology for the language he used in the match at Loftus Road on October 23 last year.
Chelsea are taking their own internal disciplinary action, which is believed to constitute a fine although the club are keeping the details confidential. It is understood Terry remains club captain.
Di Matteo admitted Terry's actions had damaged Chelsea's reputation but the club maintain they were right to stand by their player.
"The image of our club has suffered with this issue. There is no denying that," Di Matteo said.
"We try to do everything in our power to make sure we maintain high standards. People make mistakes. He has apologised and he has been punished for the language that he used.
"We have followed the legal process very closely and supported our player. He has accepted the ban now and he has realised the language he used wasn't acceptable.
"It is not like he is getting away with it. The FA have taken action against him and the club have taken action against him."
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Di Matteo said he believed the evidence Terry gave to Westminster Magistrates Court - that he was only repeating offensive words he thought Ferdinand had accused him of saying.
Terry was cleared of a racially-aggravated public order offence but his evidence was later described as "implausible" by the FA's independent panel.
"I do not (regret supporting him)," Di Matteo said.
"I do believe the evidence he gave in the Magistrates Court is exactly what happened on the day.
"He was cleared of any racial abuse in the Magistrates Court and we will take that as the result of it.
"There was the legal process with the Magistrates Court and there was the FA process. We accept both outcomes.
"He knows his language wasn't appropriate. He let himself down and the club down and he is being punished for it."
A Chelsea spokesman, sitting beside Di Matteo, added: "We put out a statement saying we would support John through the process.
"We felt that was only right and proper to do. At the end of the process the judgment was handed down by the FA and the commission.
"On that basis we have also taken action. We don't regret supporting our player through the process.
"We think that was the right thing to do. John stands behind the evidence he gave."
Chelsea have not revealed the specifics of Terry's punishment, nor confirmed exactly what he was punished for.
Was it for repeating the offensive words, which Terry had admitted to doing, or was it because the FA panel concluded he had racially abused Ferdinand?
"In either incident, we don't think use of that language is acceptable," the Chelsea spokesman said.
Di Matteo refused to confirm whether Terry would skipper Chelsea in Tuesday's Champions League tie against Shakhtar Donetsk, although it is understood he will.