The Nerazzurri boss has voiced his dismay with Sunday's events and has warned the Inter fans not to repeat their behavior.
Some of the Giuseppe Meazza club's supporters racially abused AC Milan striker Mario Balotelli during Sunday's encounter, and Moratti said their actions were unacceptable.
"I was told about the chants afterwards because I couldn't make out clearly what they were saying. I'm very sorry about what happened," the Inter president told reporters. "I'm very sorry and I really hope it doesn't happen again during the derby."
Balotelli came through the ranks of the Inter youth academy and also wore the Manchester City jersey before joining Milan in January.
He will take on his former club on Feb. 24 in the Derby della Madonnina.