Celtic have claimed their players were targeted with "sickening chants" after Rangers claimed Alfredo Morelos was subjected to racist abuse.
The Parkhead side also accused Gers fans of throwing missiles during the Old Firm clash on Sunday.
Rangers said on Monday they believe Colombia international Morelos was targeted after he was sent off by referee Kevin Clancy in the closing stages of the Light Blues' 2-1 victory, after picking up the second of two yellow cards.
Police Scotland confirmed it was investigating complaints of racist chants against a Rangers player.
A Celtic spokesman said: "We are aware of a number of incidents from Sunday's match including Celtic supporters being targeted with missiles from the away support, something which has unfortunately happened on numerous occasions previously.
"We are also aware of a number of other unsavoury incidents involving the away support, including sickening chants directed at our players and supporters.
"However, as we always do, Celtic will deal with these and all other incidents responsibly and in a dignified and professional manner and in a way which protects the greater good of the game."
The fallout from the game also saw Celtic forward Ryan Christie served with a notice of complaint by the SFA on Monday for an alleged incident involving Morelos after an hour of the game.