Terry was banned for four matches and fined £220,000 after an independent Football Association regulatory commission found him guilty of racially abusing the QPR defender Anton Ferdinand.
Terry accepted the sanctions yesterday 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."
Di Matteo welcomed Terry's decision not to appeal the four-match ban.
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 said.
"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."
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.