Terry was banned for four matches and fined 220,000 pound after an independent Football Association regulatory commission found him guilty of racially abusing the QPR defender Anton Ferdinand.
Terry accepted the sanctions on Thursday and issued an apology for the language he used, while Chelsea said they had also taken internal disciplinary action against the player, but insisted the nature of the punishment would remain confidential. Di Matteo said that Terry knows whether he remains Chelsea captain - but the manager refused to make that decision public.
"We do not discuss publicly the disciplinary matters we take against our players. They remain confidential. You will have to wait and see," Di Matteo said. "They are internal matters, the action we take against our players, and we are not going to discuss it."
Asked whether it was suitable for Terry to remain captain, Di Matteo said: "Over the many years he has been here he has shown a lot of qualities. He has realised that on that day he fell below his standards and the clubs standards.
"For that he has received a ban and a fine and more action from the club. He is being punished for what he has said. We have all made mistakes in our life before."
Terry also apologised for the language he used towards Ferdinand, although he did not specifically direct his apology to the player.
"We appreciate he has not appealed the ban and the fine and that he has apologised publicly for the language that he used," Di Matteo added.
"He has apologised generally to everyone, including the Ferdinand family. It wasn't a matter of not apologising directly. It was a matter of apologising to everyone for the language used in that game. He knows it was not appropriate and he has been banned and fined for that."
It is understood that Terry has been fined by Chelsea and that he will retain the club captaincy for Tuesday's Champions League game against Shakhtar Donetsk, despite Di Matteo's refusal to discuss the matter publicly.
Source: PA
Source: PA