Visiting fans threw smoke bombs and flares and ripped up chairs during the 5-0 rout, leaving the Parkhead outfit to foot the bill under a reciprocal agreement between clubs. Celtic could also find themselves facing an SPFL investigation when the league studies the report from match delegate Alan Dick.
The SFA no longer have any jurisdiction on such matters, as members rejected calls for strict liability at the time of the merger between the two leagues this summer.
The episode is the latest in a recent upsurge of such incidents. Motherwell's own supporters caused extensive damage to New Douglas Park last week after their Scottish Cup defeat to Albion Rovers, on the same day Rangers fans damaged Falkirk's 4G pitch with a flare, while Celtic's fans are currently under investigation by Uefa for displaying a banner against AC Milan which was deemed to be political.
"Clearly we are apalled by the scenes from last night's match and the actions of a small minority which have again tarnished the great reputation of the club and our supporters on a night when our team produced such a fantastic performance," the Celtic statement read. "We are currently investigating these events and will update our supporters early next week."
With one smoke bomb landing in the vicinity of their own goalkeeper Fraser Forster, manager Neil Lennon also criticised the night's events. "It's at our end with the goalkeeper there and it's always a worry that by accident someone could get hit or something could get by damaged by it," he said.
A Police Scotland spokeswoman said: "During the course of the match, 18 smoke bombs, three fireworks, and one flare were set off. Significant damage was caused to seats within the ground and we are looking into this matter along with the club to establish the circumstances. There were no arrests made inside the ground."
On the field, Celtic have no such problems - they have now scored 12 goals without reply away from home in their last two matches. Skipper Scott Brown, available again after a three-match continental suspension, is desperate to take that form into the Champions League meeting with Barcelona on Wednesday. "Everyone is firing on all cylinders right now and the pace in the team is incredible," said Brown.
Meanwhile, Motherwell captain Keith Lasley claims referee Steven McLean had booked him for jogging towards the match official to protest about what he regarded as a foul some 90 seconds before Kris Commons' opening goal. "Unfortunately I never got that far because the referee never let me ask him a question," said Lasley. "I might try speed walking the next time."