"Today I experienced racism during the match. Weak people try to intimidate with hate. I am not a hater and can only be sorry for those who set bad examples," Matuidi wrote on his official Facebook account.
"Football is a way to spread equality, passion and inspiration and this is what I am here for. Peace."
Italian media said that Matuidi complained to match officials during the game but no action was taken.
"You are a great player. An example to the youth," Cagliari said in a reply to Matuidi on Twitter.
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"We want to apologise to you if you were insulted at the Sardegna Arena because of the colour of your skin. Racism has nothing to do with the Sardinian people. Only ignorance can explain certain behaviour. Respect."
Serie A's disciplinary tribunal usually announces sanctions on the first working day after a full round of matches has been completed, meaning the incident is likely to be dealt with on Monday.
Last week, Verona were fined 20,000 euros (£17,731) and given a suspended partial stadium ban after supporters racially abused Matuidi following his opening goal during Juventus's 3-1 away win on Dec. 30.
Serie A's disciplinary tribunal said that Verona's Curva Sud (South Curve) would be closed for one match if there was a repeat incident within a year.
Matuidi, who has 62 caps for France, joined Juventus before the start of the current season and has scored twice, both in the league, for the Italian champions.
Cagliari were also involved in an incident last season when Ghanaian midfielder Sulley Muntari walked off in protest during a match for Pescara away to the Sardinian side.
Muntari said the referee had booked him for dissent when he complained about racist abuse from some fans. He was given a second yellow card for leaving the pitch without permission, triggering an automatic one-match ban which was later overturned by the Italian football federation (FIGC).
Serie A's disciplinary tribunal took no action against Cagliari, saying that only around 10 supporters were involved in abusing Muntari.
(Reporting by Aditi Prakash in Bengaluru and Brian Homewood in Berne; Editing by Toby Davis and Clare Fallon)
