Eight people have been arrested after Sunday's Old Firm match with Rangers criticising the policing in the aftermath of the game at Celtic Park.
Officers say the arrests were made in connection with various offences including disorder, pyrotechnics and religiously aggravated offences.
Police also confirmed two of the arrests were within the stadium itself with the match kicking off at 12pm on Sunday May 1.
A police statement added they were aware of missiles being thrown in the stadium between football fans on each side.
One of these also struck an officer, however they were not seriously injured.
It comes as a Rangers spokesperson released a statement explaining their disappointment at match's policing.
The club said on Sunday evening: “We are disappointed with the Police response after the Old Firm at Parkhead today.
"Our support was left unprotected as they were attacked by bottles and other missiles.
"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.”
Police Scotland said they are still carrying out enquiries and asked anyone with information to get in touch with them.
Chief Superintendent Stevie Dolan said: "Police Scotland had a proportionate plan in place to support the safety operation led by Celtic FC at Sunday’s match, between Celtic and Rangers at Celtic Park, and to deal swiftly with any acts of violence, disorder and anti-social behaviour.
“I would like to thank the vast majority of fans who enjoyed the fixture and followed club and police advice.
"Eight people were arrested for various offences including disorder, pyrotechnics and religiously aggravated offences. Two of these arrests were within the stadium.
“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 serious injured.
“Any reports we receive from members of the public relating to match related incidents will be investigated.
“Further enquiries 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.
“Anyone with any information relating to any of these incidents should contact Police Scotland via 101.”
A spokesperson for Celtic FC said: “We are still working through the recent events at Ibrox, including the assaults on our staff members and supporters.”
“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.”
“We will be liaising with all relevant parties in order that a wide range of issues are fully addressed in the appropriate manner.”
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