Alex Dyer has vowed Kilmarnock will "eradicate" racism from Rugby Park after the Ayrshire club launched a probe into alleged abuse directed at Rangers striker Alfredo Morelos.
TV cameras appeared to capture a shout aimed at the Colombian during Wednesday's Scottish Premiership game.
Kilmarnock have vowed to ban anyone found guilty of discriminatory insults.
"If we can find the person who did this they will obviously be banned from the football club," manager Dyer said.
"I didn't hear it on the night, but if that is the case, I know the club will look into it. We won't tolerate anything like this."
Dyer is the only black manager in the Scottish top flight and he does not want his club's reputation tarnished by one individual.
"We also know this isn't just about football," he said. "It's society's problem, but at the end of the day, we don't want anyone with that mentality around this football club."
Dyer believes allegations of racism run contrary to the impression he gained about Kilmarnock - the club and the town.
"Kilmarnock have been brilliant," he said. "The club has given me a opportunity to manage it. As you can see, I'm a black man, but that never came into it at all. I was hired because of my ability and long may that continue.
"This is a great football club and a great town to live in with good people. One or two aren't going to spoil it for the rest. If people do have those thoughts, we'll eradicate it from this football club."
Kilmarnock have urged anyone with information about the alleged incident to come forward.
"The club is aware of an incident of alleged racism against Alfredo Morelos and will investigate this matter fully," they said in a statement.
"Kilmarnock Football Club wholeheartedly condemns any form of racism and anyone found to be involved in incidents of this nature will be immediately banned from Rugby Park."