Rangers claim fans were "attacked by bottles and other missiles" at Celtic Park on Sunday, with the club also set to report "possible hate crimes" to Police Scotland.
The Ibrox club say they have received reports of injuries to elderly and disabled supporters.
Rangers drew 1-1 with Celtic in the cinch Premiership encounter, which kept the Hoops six points clear of their Old Firm rivals at the top of the table with three fixtures remaining.
In a statement, a Rangers spokesperson said: "We are disappointed with the police response after the Old Firm derby 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."
In a Celtic statement by way of response, the Parkhead club referred back to the trip to Ibrox last month when at half-time in the 2-1 win a member of their backroom staff was allegedly struck by a glass bottle which required him to have stitches.
The statement also claimed that Hoops fans were "targeted with missiles" at Celtic Park.
A spokesperson for Celtic 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."
Police Scotland have been contacted for comment.