The supporters held an unauthorised protest march against an anti-sectarianism law last weekend.
A total of 13 people were arrested for alleged public order offences, near Glasgow Cross, as they made their way to a match at Celtic Park on Saturday.
The force today pledged to provide evidence of "the levels of aggression and abuse police officers were subjected to" during Saturday's events.
Officers are currently reviewing CCTV evidence of the protest march, which is said to involve members of the Green Brigade.
In a statement released today, Strathclyde Police said: "Any accusations regarding the police response to the illegal procession in the Gallowgate are inaccurate.
"We are currently reviewing a significant amount of CCTV footage captured on the day.
"This clearly shows the instigation of the incident, the levels of aggression and abuse police officers were subjected to and the restraint demonstrated by officers in very difficult circumstances.
"Although we are satisfied our officers conducted themselves in a professional and proportionate manner, we can assure the public that we will investigate any complaint thoroughly."
Today's statement follows Justice Secretary Kenny MacAskill dismissing calls for an independent inquiry.