Celtic manager Neil Lennon has urged supporters not to spoil the club's reputation after reports of trouble at the St Stephen's Day clash with Dundee.
Celtic chief executive Peter Lawwell apologised to Dundee and promised strong action after a number of supporters were ejected from Dens Park during the evening encounter, which Celtic won 2-0.
Lennon said today: "We have a fantastic reputation wherever we go and we are very proud of that and we want to preserve it.
"Don't tarnish the reputation of the club please."
If you are thinking about doing it, then we would rather you didn't come."
Dundee operations manager Jim Thomson said there was "serious disorder" in the stadium concourse and "widespread" drunkenness.
Police reported five supporters, including four away fans, to the procurator fiscal, while the home club said many more were ejected.
Thomson told several national newspapers: "I have never seen anything like the behaviour of the Celtic fans in the 20 years I have been running games at Dens Park.
"The situation was almost unmanageable and I have never seen so many people drunk.
"Our fans were abused, our stewards were abused and no doubt the police were abused. The turnstile operators were visibly shaken.
"The away fans had no respect for their surroundings, they were doing the toilet where they stood.
"I had Celtic fans come up to me to tell me they were embarrassed by their fans' behaviour."
Lawwell responded in a statement: "Clearly, we apologise to Dundee Football Club. We will work with them and look into any incident which is raised and if we can identify any individuals involved, we will obviously take the strongest possible action.
"We have received a number of complaints from our own supporters about the conduct of this minority. We cannot allow our supporters' enjoyment of our matches to be affected in this way and we will not sit and allow the club's reputation to be damaged."