Humza Yousaf says Rangers could have given stronger messaging to fans to prevent the scenes in Glasgow on Saturday.
The Justice Secretary credited the club for continuing to communicate with the authorities following the violence and breach of covid rules at the weekend.
Around 15,000 Gers fans descended on Ibrox Stadium and then George Square to celebrate their side winning the Scottish Premiership title.
Broken glass, destroyed memorial benches and litter strewn across the city centre was seen by Glasgow City Council cleansing workers on Sunday morning when they cleaned up the mess.
So far more than 20 people have been arrested following the scenes in George Square on Saturday.
Answering an urgent question in the chamber, Yousaf said: "Since the weekend my officials and I have continued to liaise with Police Scotland and engaged with Rangers Football Club directly to discuss the fallout.
"In fairness to the club, they have engaged for a number of weeks with the Scottish Government with Glasgow City Council and they released a statement asking their fans to respect the covid guidelines.
"What I would say is I would have liked that messaging to have been more explicit and stronger but nonetheless that messaging did come forth.
"Lets not forget, the responsibility of those dreadful scenes lies on the shoulders of those individuals who took part in that disorder. There must be personal responsibility.
"Police Scotland will follow up."
Police Scotland has vowed to make more arrests following the violence.
Detective Inspector Craig Warren, who is leading the investigation, said: “The public can be confident we are doing everything possible to identify those responsible for the violence and disorder on Saturday.
“This will take time due to the numbers involved. Rest assured, if you were involved in causing this disorder, violence or anti-social behaviour you will be arrested.
"We are reviewing CCTV, video and still images and I would appeal to anyone who may have captured incidents on their mobiles to please get in touch with us.
“You may have footage that could help us in our investigation and it’s vital we speak with you.
"The Major Incident Public Portal (MIPP) is now available for the public to send any information, photographs or images directly to the investigation team.
"There has been footage circulating on social media covering the events in George Square. If you recognise people involved in these acts of violence and disorder, please let us know.
“You can contact 101 or alternatively contact Crimestoppers anonymously on 0800 555 111.”
