Hamilton Academical chairman Allan Maitland told fans who directed “despicable abuse” at players and management in the play-off against Alloa that they were not welcome at the club.
Boss John Rankin spoke of a “personal” comment to his family afterwards.
“If you are unable to control your emotions or feel the need to be overtly abusive, please do not come to games – you are not welcome,” Maitland said.
“I understand that sometimes it’s necessary to vent frustration – but there is a line where venting that frustration becomes intolerable and totally unacceptable, and we achieved that on Saturday.
“Several supporters shouted despicable and abusive comments at our management team and directors which were disgusting and unacceptable in any environment at any time, let alone a football game where families and young children are present.
“We are working to identify those responsible for this hate crime and these so-called supporters will receive the banning order they deserve from all football matches.”
Five Hamilton goals – a hat-trick from Andy Winter and a brace from Dario Zanatta – in 15 minutes turned the Scottish Championship semi-final at New Douglas Park in favor of Rankin’s men, who will face the Airdrieonians over two legs to determine who will play in the second division next season.
“We are a club known for succeeding in adversity and if we hope to succeed and maintain our position in the Championship, we need everyone pulling in the same direction,” added Maitland.
“I ask all fans to give their full support to the players – as Saturday showed, anything can happen in a football match.”