Alan Leighton, the national secretary of Prospect, said the FA must act to protect the Respect campaign.
Leighton said: "I don't know what Sir Alex earns but a small fine or a touchline suspension would be like water off a duck's back to him so I think there has to be some recognition that this is a serious allegation that needs to be properly dealt with and punished severely.
"There are issues around suspension from the job, that would be new territory that hasn't happened before but I think the FA has to grab the nettle on this one.
"Because a small fine or a large fine would be like water off a duck's back, there has to be some sort of punishment that is going to stop people from doing this or otherwise we are going to see more and more of it.
"We have to be talking about punishments that are going to really lead to a change in behaviour."