Linfield have said they are trying to identify the people guilty of racist and sectarian chanting during the match against Shelbourne on Monday night.
Linfield celebrated a 2-0 Setanta Cup win over Linfield
The club vowed that if they could find out who the culprits were, they would be banned from the Windsor Park ground.
"It was highly offensive to players, staff, management committee and all real supporters of the game from both clubs," said a Linfield statement.
"This appalling behaviour from a small crowd sector will not be tolerated."
Linfield added that they had set up a working party to identify and exclude from the offenders.
"The vast majority of our supporters are to be congratulated for coming on such a wild evening to give support on an otherwise great night," the statement added.