Linfield have launched an investigation into a "number of incidents" during Friday night's Big Two derby at Windsor Park.
The club says it will take "robust action" on anyone found guilty of misconduct inside the stadium.
The Blues issued a statement on Monday, while manager David Healy also addressed the alleged incidents during his post-match press conference on Friday night.
Read more: Money talks as Linfield boss David Healy outlines "monumental" challenge
The club said: "Linfield Football Club is conducting a thorough investigation into a number of incidents which occurred in the stadium during Friday's Premiership game against Glentoran.
"If any evidence of misconduct is uncovered and individuals are identified, then the club will not hesitate to take robust action against those involved, including referring evidence of any possible criminal acts to the Police Service of Northern Ireland."
Meanwhile, manager Healy insists anyone attending an Irish League match must "maintain a level of civilisation".
He said on Friday night: "They need to act as if they are civil human beings. Sometimes in football, and other sports, people let themselves down.
"Nobody wants to league the thrive as much as myself. Managers want this league to thrive.
"They want people that when they go to football events, sporting events to be civilised and understand that there are different sorts of personalities at the game - i.e. wives and kids, mums, dads and there is always the danger that somebody gets put off coming to the games.
"I hope that sporting events going forward, football matches in this country, that we can have a civilised understanding."
READ NEXT:
- Support of Glens helped McMenamin deal with historic video fallout
Mick McDermott hails 'real specimen' Purkis after Big Two heroics
Championship game abandoned following serious injury to player
Everton FC star's goal celebration was 'promise' to Belfast football club
Sign up to our free sports newsletter to get the latest headlines to your inbox.
