Celtic have suspended three fans amid a police investigation into complaints of anti-social behaviour before and during their Scottish Cup tie at Stranraer on Sunday.
The police probe will focus on the use of pyrotechnic devices, smoke bombs and fire crackers which were set off within the terraces as well as being thrown onto the pitch at Stair Park.
It will also concentrate on the alleged singing of sectarian songs during the match, which Celtic won 3-0.
Four supporters were arrested for football related and public order offences inside and out of the ground before Celtic, who could face possible sanctions from the SFA over the disruption, issued bans to the three fans on Monday afternoon.
In a statement, Superintendent Steven Lowther, the match commander, said: "The behaviour of a minority on the day was unacceptable.What was supposed to be an enjoyable event for all was tarnished by a group of individuals who were intent on singing sectarian songs as well as letting off smoke bombs and pyrotechnics within the crowd.
"It is evident that those involved had no concerns for either the safety of others or how their behaviour spoiled what should otherwise have been an event where the post-match discussion should have centred on football and not their antics.
"We will work with partners and both clubs to try and identify those involved to ensure positive action is taken to address the scenes which were witnessed at Stair Park."
Celtic have launched their own investigation and condemned the actions of the minority of fans who "have again caused embarrassment to Celtic", claiming "they simply do not care about our club."
In a statement, they said: "We will not allow safety to be compromised by the actions of a tiny minority.
"We have been inundated again by our supporters following yesterday's events and those fans can rest assured that this issue will be dealt with in the strongest terms.
"We cannot and will not allow this minority to destroy the magnificent reputation which our fans have earned over many years."
The Scottish champions were charged by UEFA for setting off flares during a Europa League match against Fenerbahce in December and manager Ronny Deila has admitted: "it's something that is making a bad reputation for the club."