"Police had worked closely with the bereaved family involved to ensure that the funeral service and interment passed off without incident", chief inspector O'Connor said.
A 42-year-old man, arrested on suspicion of common assault and possession of an offensive weapon in a public place, has been released on police bail pending further enquiries.
It broke out at about 15:00 GMT on Monday on North Circular Road.
POLICE IN NORTHERN Ireland have now arrested a total of four people in relation to a stabbing incident that took place after a funeral in Armagh yesterday.
Three people have been taken to Craigavon Area Hospital with cuts that are not believed to be life threatening.
The 23-year-old man arrested on Monday was questioned on suspicion of grievous bodily harm with intent and possession of an offensive weapon in a public place.
"It was also deeply upsetting for the grieving family", he added.
A 23-year-old man arrested in the wake of the incident at St Colman's cemetery on Monday afternoon has been released on bail pending further inquiries.
A 20-year-old man was arrested today on suspicion of grievous bodily harm and possessing an article with a blade in a public place and a 37-year-old man was arrested on suspicion of common assault and possession of an offensive weapon in a public place.
Officers remained at the graveyard last night amid fears of further disturbances.
The PSNI said that a "prolonged altercation" took place on the North Circular road in Lurgan after a funeral.
"I can not believe that something like this would happen in Lurgan and in particular at a funeral", she said.
"I urge anyone with any information to come forward to the police immediately".