Officials have warned future parades face greater restrictions or even prohibition after police launched a probe into the incident.
Footage emerged online of people singing the anti-Irish “Famine Song”, while a band played along, during what appears to be the annual celebration on Saturday.
A spokesman for Glasgow City Council said: “The European Convention on Human Rights enshrines the rights to peaceful assembly and freedom of expression.
“However, these rights are not absolute. They must be balanced by the responsibility to ensure the rights of others are not infringed.
“As with all public processions, there will be a debrief involving Police Scotland, the organiser and the council. The council will take into account any issues of public disorder, anti-social behaviour or damage to property resulting from the procession.
“It will also take into consideration any evidenced issues and, if a future procession notification is received from the organiser, the likelihood of any restriction or prohibition may be greater.”
The song, sung to the tune of the Beach Boys’ track Sloop John B, has previously been ruled to be racist by a Scottish court.
David Scott, campaign director for anti-sectarian group Nil by Mouth, said: “If they [The Orange Order] are a religious and cultural organisation, what would be the relevance of a Beach Boys song?
“We know that tune also has another certain set of lyrics. The organisers should be speaking to band members and saying what is acceptable.”
The main County Grand Orange Order parade from George Square to Glasgow Green saw 4,500 people in 63 bands take part and another 4,000 spectators.
It was in celebration of Prince William of Orange’s victory over King James II at the Battle of the Boyne in 1690.
Eight arrests were made on Saturday for alleged minor disorder and alcohol-related offences.
Robert McLean, executive officer for the Grand Orange Lodge of Scotland, said: “At the end of the day, members of the public will sing songs to tunes.
“I have been quite clear - if police investigate we will assist with their inquiries. We look forward to the debrief and looking at any incidents that occurred.”
A police probe was launched after the footage emerged.
Chief Superintendent Brian McInulty said: “Saturday’s policing operation primarily focused on the safety of the public during the parades. Police Scotland, however, operates a zero-tolerance policy when it comes to any form of sectarian abuse and will fully investigate any incidents brought to their attention.”