Portadown FC has said it told police on Tuesday afternoon a busload of people was being organised to cause trouble at that night's match with Glentoran.
Two Glentoran coaches received medical treatment after a firework exploded near their bench during the cup game.
On its website, Portadown said it again contacted police on arrival in east Belfast but was told nothing could be done as no offence had taken place.
The club said it was surprised fans were not searched going into the Oval.
Police have said Glentoran Football Club was responsible for searching fans entering the grounds and for stewarding inside the ground.
Portadown FC added: "When the first firework was thrown, club stewards immediately took action to identify and observe the person(s) responsible.
"A request to the police for assistance was refused.
"When the second firework was thrown the club secretary and a director of Portadown FC confronted the group involved and faced them down to prevent further trouble with the assistance of club stewards.
"At this stage a second request for police assistance was refused on operational grounds, stating a lack of manpower and resources as the reason."
After the stadium had been cleared after the game a small box of eight fireworks was found, and handed over to police.
Photographs of the alleged offenders were taken by Portadown stewards and will be given to the police.
"We can confirm that as of Thursday afternoon, one of the offenders observed throwing a firework has been identified and his name and address has been passed to the PSNI.
"This individual will be given a lifetime ban from Shamrock Park (Portadown's home ground), as well as facing potential criminal charges," the club said.
"Portadown FC will continue to work with the PSNI, IFA and Glentoran FC to identify those involved in these acts of hooliganism."
In a statement police said: "In relation to this game, we had extra resources dedicated to policing the area outside the grounds for this football match.
"On this occasion when asked for assistance, a decision was taken that it would not be appropriate for police to enter the grounds amidst hundreds of fans to effect arrests in the middle of the game.
"Instead, at the end of the game police liaised with stewards and are currently actively investigating the incident and will be working with the club on viewing CCTV footage to identify any other persons involved."
They said a man was arrested for disorderly behaviour and possession of an offensive weapon. He has since been released on bail pending further enquiries.
Glentoran's goalkeeping coach, David McClelland, was knocked to the ground as the firework blew a contact lens out of one eye, while another coach, Pete Batey, was treated after it went off near his ear.