Terry was banned for four matches and fined £220,000 after an independent Football Association regulatory commission found him guilty of racially abusing QPR defender Anton Ferdinand.
Asked whether it was suitable for Terry to remain captain in the circumstances, 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 club's 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."