Falkirk are "extremely disappointed and embarrassed by the disorder" outside their ground after the SPFL Trust semi-final defeat by The New Saints.
The Bairns lost 1-0 to the Welsh side at the Falkirk Stadium on Saturday.
The Scottish League 1 leaders say they "have apologised to The New Saints and their supporters for the inevitable distress caused".
"This type of occurrence is previously unknown at our stadium and will not be tolerated," Falkirk said.
"Anyone identified will be made known to police and will receive the most severe sanctions from the club.
"We wish to thank the vast majority of Falkirk supporters who attended the game on Saturday, once again in great numbers, for your fantastic backing and the positive atmosphere which you created."
TNS will play Airdrieonians in next month's final.