The Young Conway Volunteers band had been banned from parading past St Patrick's Church on Donegall Street in the city after being filmed playing an allegedly sectarian song at the spot during July 12 demonstrations.
Violence broke out in the area on Saturday as the Shankill Road band marched past the church.
"Their behaviour is not worthy of our city, nor of the Christian ideals espoused by the Royal Black Preceptory and other organisations involved," Bishop Treanor said.
The senior cleric also criticised senior unionist politicians who had signed a letter calling for the replacement of the Parades Commission.
"The one-sided nature of this letter and the failure to acknowledge past and present behaviours that give rise to just opposition to such marches in a small number of areas, reflects a failed, partisan and unjust politics of the past," he said.
He also asked for police to explain their actions yesterday, claiming there was a lack of visible effort to enforce the commission's determination.
The bishop added: "As we seek to build that more tolerant future together, all public anniversaries should be shaped as moments for courageous leadership and new vision, rather than for encouraging hatred or for creating the conditions which might provoke violence. It is long since time to stop reverting to the intolerant and disrespectful ways of the past. It is time to consolidate and sustain respect for all traditions in our society, and particularly on occasions of commemoration. It is time to foster freedom of religion for all and respect for every church, temple and place of worship without exception. It is time to leave provocation behind us. Critically, it is time to shape for our youth, our children and future generations, mentalities and patterns of respect for one another as citizens and human persons."
Seven police officers were injured in Saturday's disturbances - none seriously. A number of bands played music between Clifton Street and Unity Street area, which police also said was a breach of a ruling by the Parades Commission adjudication body.
It is understood police were attacked when they attempted to keep nationalists opposed to the parade and loyalists apart.
Bottles were thrown from both sides during the trouble.
A female officer required hospital treatment after sustaining a head injury.
Police today confirmed three arrests had been made following the trouble.
A 13-year-old boy was arrested around 12.15pm in the Donegall Street area on suspicion of riotous behaviour. He was released pending a report to the Public Prosecution Service.
At around 5.45pm, a 38-year-old man was arrested in the North Queen Street area on suspicion of disorderly behaviour and provocative conduct.
He remained in custody yesterday.
Shortly after 6pm, an 18-year-old man was arrested in the Clifton Street area on suspicion of disorderly behaviour and assault on police.
He has been charged with both offences and is due to appear at Belfast Magistrates Court on Thursday 20 September.
The Parades Commission imposed the restrictions, which were unsuccessfully challenged in the courts, on the band for the Royal Black Institution march.
Assistant Chief Constable Dave Jones, head of the policing operation, yesterday said anyone who defied the ruling will be pursued.
"It is our assessment that there have been breaches of the Parades Commission determination and I can assure everyone that we will be working to bring those believed to have breached it before the courts," he said.
"We have gathered the evidence required to do so."
In response to the Parades Commission ruling being defied, a spokesperson for the body said its decision was fair and balanced.
The 38-year-old man arrested in the North Queen Street area on suspicion of disorderly behaviour and provocative conduct has been charged with both offences.
He is due to appear at Belfast Magistrates' Court this morning.