Dozens of people were filmed singing “The famine is over, why don’t you go home?” after the Rangers beat Old Firm rivals Celtic 1-0 at Ibrox.
Police have since launched an investigation into the incident, but came under fire on social media amid accusations that officers did not intervene at the time.
But in a statement on Monday, Assistant Chief Constable Bernard Higgins defended the force’s actions, insisting that anti-Irish bigotry was “wholly unacceptable”.
“Officers on patrol came across this group as it was making its way through Glasgow City Centre,” ACC Higgins said.
“Due to the numbers and to ensure public and officer safety, additional officers were called to assist and, at this point, individuals' details were noted and the group dispersed.
“We did not facilitate this event and to say so is inaccurate,” he added.
Officers are now understood to be pursuing a number of lines of enquiry, including reviewing CCTV footage and videos posted on social media.
ACC Higgins said: “I fully expect a number of arrests to be made.
“This type of anti-Irish Catholic behaviour is wholly unacceptable. Our enquiries are ongoing to identify those who were involved and we will take the appropriate action against them.
“We would ask anyone who has any information that could assist our investigation to contact us.”
He added that the challenges of the sectarianism still evident in some parts of Scotland are “a much broader societal problem” and that, “whilst policing will have a role to play in addressing the symptoms, its causes are a problem which require a more effective, joined-up, civic response.”
On Sunday, Pressure group Call It Out, which campaigns against anti-catholic bigotry and anti-Irish racism in Scotland, called on the Scottish Government and Glasgow City Council to take action and to “start by recognising our community”.
The group tweeted: “This is the kind of racism you don’t notice – day after day, week after week, year after year, decade after decade. When are you going to call it out?”