On Saturday masked men made their way from the Kilwilkee estate to St Colman's Cemetery.
The men were dressed in paramilitary uniforms and were carrying republican flags.
Speaking to the Belfast Telegraph yesterday, Kate Carroll said: "This time of year was always going to be controversial, but Easter is meant to be a holiday time and a time for children to enjoy. We don't need this type of activity. This is not needed and it should never have happened."
She hit out at the actions by the masked men who appeared as part of an Easter Rising commemoration parade.
She added: "If this was a show of strength and they were out marching, why didn't they march without their masks. If they feel that they are fighting a war, why not come out like proper soldiers and show their faces?"
Local unionist politicians called on the police to take action.
Armagh, Banbridge and Craigavon District DUP councillor Carla Lockhart condemned those who staged what she termed a "republican show of strength".
"This is deeply concerning. The days of masked men parading through our streets should be gone.
"This has no place in the new Northern Ireland," she said.
First Minister Arlene Foster said she had warned that dissident republicans would use the events of Easter 1916 to legitimise their warped actions in 2016.
"This is further proof I was right," she said. "Violence was always wrong."
Police were not present at the parade but it was observed from above by a PSNI helicopter.
TUV Assembly candidate Roy Ferguson said: "The events on Saturday afternoon underscored once again that there are parts of Lurgan where republicans effectively do as they please.
"This is totally unacceptable and I will be contacting the PSNI to demand an explanation as to why the terrorist show of strength was permitted to take place and how they propose to bring those involved before the courts."
PSNI Superintendent Paul Reid said: "Police are aware of a small unnotified parade which took place in the Kilwilkie area of Lurgan on Saturday afternoon, March 26. Organisers of parades are required to give formal notification of their intentions.
"An investigation into this incident is under way and enquiries are ongoing."
Meanwhile, a masked man has said the Continuity IRA, which claimed the murder of Mr Carroll, will continue its attacks on the security forces.
Speaking at a commemoration in Carrickmore, Co Tyrone, on Saturday he said: "We pledge our resolve to continue the struggle against British rule. The volunteers of the Continuity Irish Republican Army will continue to strike at will at the British forces of occupation. That is the most fitting tribute we can make to the men and women of 1916."