Police are investigating the claim that a visiting player was abused after Barnsley's 2-1 win and Millwall say anyone found guilty of racism will be given a lifetime ban.
The incident remains under investigation.
The following day in London, Chelsea player Antonio Rudiger was allegedly racially abused in his side's derby with Tottenham Hotspur, with play stopped after the defender heard monkey noises.
Meanwhile, a Chelsea fan has been arrested for allegedly abusing Spurs' player Son Heung-min.
Rose said: "Everything is fine. Millwall have been great in the situation and reported it straight after the game. I am sure they are pretty keen to clear up their own image. It is quite clear around the ground that is what they are trying to do.
"They are really on top of it and the police are involved and it is under investigation.
"It is a problem in society and football does enhance that problem. It has to be dealt with, not just in football, but in society. It is a complete new topic to be debated about. Of course, it is unacceptable.
"In a football ground, you have a social gathering. Without being condescending, it is always about education. We can educate the community, which the club is trying to do. But ultimately what goes on behind closed doors with families and parents and friends, that is how you address that.
"Football can bring out the worst in people, which is not the best advert for the sport. You can give people a few drinks and losing a game can bring out the worst in some people.
"My wife and my dad went and everywhere around the stadium, there was this (anti) hate campaign and I know they (Millwall) don't want it. It does not matter, we can talk until we are blue in the face and talking for years and years.
"Something has got to change..How does it change? That is the biggest question."