Garvan O’Doherty said the Parachute Regiment insignia with the letter ‘F’ breached an agreement reached ahead of Saturday’s parade.
It was worn by members of Clyde Valley Flute Band from Larne.
The Apprentice Boys said they recognised the potential upset caused by the emblem.
Mr O’Doherty, who has been involved in parades discussions for two decades, said he attended meetings with Bogside residents and Apprentice Boys both in early July and again in early August.
“We all agreed at the meeting we didn’t want political or sectarian messages and we all agreed that we would do all that we can to make sure that didn’t take place,” he said.
“Clearly, this band slipped through, one band out of 145 chooses to cause a bit of turmoil. We can’t let the band ruin the process; we cannot let this process be derailed.”
He added: “I wouldn’t have them about the city anymore.”On Tuesday evening, the Apprentice Boys governor, Graeme Stenhouse, said the loyal order had “no prior knowledge of the band’s uniform, or this incident, until the conclusion of the main parade on Bond Street”.
“We recognise this may have caused upset to many in the nationalist community,” he said.
Police had escorted the band during Saturday’s parade and later stopped the band’s bus.
Mr Stenhouse said the parade should not be used as a means to “heighten tensions in a shared city”.
The governor again rejected claims that an agreement about symbols supporting the Parachute Regiment had been put in place before the march.
“This agreement never took place,” he said.
“We would never place our marshals under such difficult circumstances.”
The DUP and UUP met PSNI officials separately on Tuesday to discuss Saturday’s policing operation.
Democratic Unionist Party leader Arlene Foster said that a lot of loyalists are concerned by the police approach.
UUP leader Robin Swann said the police “intervention could’ve been handled in a completely different way”.Deputy Chief Constable Stephen Martin said he had “listened carefully to all the strong concerns that have been raised” and that there will be a full debrief of the force’s actions.
Clyde Valley Flute Band said that the symbol on their shirts was an expression of “a legitimately held view which they are entitled to hold”.
The PSNI are now preparin a file for the Public Prosecution Service to see if the band breached public order laws.