Scenes described by Hoops boss Brendan Rodgers as a “melee” met Scott Brown’s injury-time winner, with visiting fans spilling onto the field of play to celebrate with the players.
Images showing scores of damaged seats in the away end emerged after the match, while flares were lit and thrown at the start of the match - all of which could be probed by the authorities.
Killie striker Kris Boyd was hit by a coin while he warmed up in front of the Celtic fans and there were reports of sectarian abuse being aimed at the veteran forward as well.
Speaking after the match, Rodgers said: “Supporters had come on to the pitch, which we don’t want to see. I understand the emotion of it all. “But I didn’t see so much of it, I had to reorganise very quickly because we were down to ten men.”
He did, however, condemn the incident with Boyd, adding: “Any behaviour like that is not acceptable at all, I think we would all reinforce that.”
Rodgers’ opposite number Steve Clarke added: “You are always concerned when fans come on the pitch like that. “In a sort of backhanded way, the celebrations were probably a little bit over the top and it is a big compliment to Kilmarnock that Celtic come here and celebrate a victory like that.”