Police Scotland is investigating "significant damage" to the Fir Park seating, while fireworks, smoke bombs and a flare were set off in the away end.
Celtic have already begun their own enquiries into the "appalling" events, and now influential fan group the Green Brigade has made it clear it does not condone Friday's trouble.
A statement read: "We as a group are as disappointed as any about such indefensible behaviour and regret that it happened on our watch.
"Whilst it was not members of our group behaving in this manner, we accept the fact that these actions took place behind our banner in what was an unofficial 'Green Brigade section'.
"It is particularly disappointing given how hard we have worked as a member organisation of Fans Against Criminalisation and of our own accord to fight the criminalisation of football supporters as we realise the damage that the events of Friday night could have on our efforts to challenge the continued harassment of Celtic fans by Police Scotland.
"Ultimately, we should have had greater control of the bodies present within our block and our failure to do so has resulted in events which are unacceptable."
The main Celtic fans' group, the Affiliation of Registered Celtic Supporters Clubs, issued its own statement.
It read: "We should be discussing another devastating Celtic performance on the pitch instead we are talking about disappointments off the field.
"Lets make no mistake that incidents like Friday night at Fir Park and the publicity that this attracts makes any negotiations regarding ticket pricing, safe standing and policing at games more difficult."