The Clyde Valley Flute Band from Larne was stopped from taking part in the return leg of the parade on Saturday after members had Parachute Regiment emblems and the letter ‘F’ on their uniforms.
Said Mr Eastwood: “Derry has been a model of respect, reconciliation and leadership when it comes to parading. Communities have sought to secure mutual accommodation, even when relationships have been tense.
“It is a matter of profound regret that a band chose to march on the streets of this city displaying a motif of the Parachute Regiment on their uniform.
“This has caused deep hurt and distress to many victims in Derry.
“The Apprentice Boys need to understand how people feel about this.
“They need to listen to the voices of those who have been hurt.
“We have requested a meeting with the Apprentice Boys to convey the very real pain that people are feeling and to help them understand the effect that this decision has had on community relations in our city.
“It is my sincere hope that we can return to the space of accommodation, understanding and respect,” added the Foyle MLA.
The Clyde Valley Flute Band’s bus was stopped outside the city by police and members were spoken to by police.
The PSNI said it was investigating the behaviour and symbols displayed by one band.
A spokeswoman said a report would be forwarded to the Public Prosecution Service (PPS).
She also added that a number of individuals would also be reported following an “unnotified protest”.
Police said five people were arrested on suspicion of public disorder offences during the day.