Rangers said its supporters had been left “unprotected” and that elderly and disabled fans had been injured by bottles and other missiles.

Celtic said its supporters and stewards were also hit by debris, including seats ripped from the stands.

Police Scotland said its plans had been “proportionate”.

A total of eight people were arrested for various offences including disorder, pyrotechnics and religiously aggravated offences.

Ch Supt Stevie Dolan said: “We are aware of missiles being thrown between groups of supporters within the stadium, one of which struck a police officer who thankfully was not seriously injured.

“Any reports we receive from members of the public relating to match-related incidents will be investigated.

“Further inquiries into disorder on Fielden Street before the match are being carried and we will continue to work in partnership with football clubs to ensure that such events take place safely.”

In a statement after the match, which ended in a 1-1 draw, Rangers said it was “disappointed” with the police response.

“Our support was left unprotected as they were attacked by bottles and other missiles,” it said.

“Reports so far include injuries to elderly and disabled supporters. Furthermore, we are collating evidence of possible hate crimes which will be reported to Police Scotland as a matter of urgency.

“We intend to raise our concerns with Police Scotland and Celtic during the debrief.”

Celtic said it was still “working through the recent events at Ibrox”.

During a match last month, a Celtic physiotherapist was hit on the head by a glass bottle and glass had to be removed from the Celtic penalty area.

“It is extremely regrettable that again our supporters have been targeted with missiles, including bottles and seating, ripped from our seating deck, resulting in injury to fans and stewards,” said Celtic.

“We will be liaising with all relevant parties in order that a wide range of issues are fully addressed in the appropriate manner.”

The fallout from the most recent meeting between Scotland’s two biggest clubs will probably surprise no-one. The avalanche of post-match statements relating to fan behaviour has become depressingly predictable.

In the last three fixtures alone we’ve witnessed bottles being thrown, a member of the Celtic backroom team needing treatment, broken glass being cleared from the pitch, fireworks being set off inside and outside stadia, widespread sectarian singing, seats being ripped up and used as missiles and various arrests for disorder.

The government has adopted a hands off approach – it has tried legislation in the past and it failed.

The police say they can’t deal with the problem on their own and the football governing bodies shy away from tougher sanctions for the clubs.

In European competition, heavy fines and even stadium closures are used as a deterrent.

Strict liability is something that is in place in many European countries where clubs can take a harsher line on unacceptable conduct. Scottish clubs have so far failed to adopt that.

If clubs can prove they’ve taken reasonable measures to prevent unacceptable conduct, then little to no action is taken. The reality is, if the clubs who issue statements demanding tougher action really want it, the power is in their own hands.