Police have arrested and bailed a 25-year-old man from Cheltenham on suspicion of sending racist tweets to Northampton Town striker Adebayo Akinfenwa and defender Clarke Carlisle.
A joint investigation between police forces in Gloucestershire and Northamptonshire was launched on Wednesday night.
It comes after Northampton knocked Cheltenham out of the League Two play-offs over two legs last Thursday and Sunday.
Carlisle, who captained Northampton in both matches, is also chairman of the Professional Footballers’ Association and an ambassador for anti-racism campaigners Kick It Out.
In response to a racial tweet, Carlisle wrote: “Really?! You must make your parents very proud.”
Cheltenham Town said if proceedings continued and the man was found guilty of racist abuse, they would make an example of him.
Mr Baker said: “It is, of course, totally unacceptable and, if he is proven guilty, the club will be taking its own action to ban him from home games in the coming season.
“It’s not something we have discussed as a board as yet but we do take crowd behaviour very seriously. I think there’s a racist culture in British society per se and it comes out in various ways, including football. I don’t think it’s a football problem but a small collection of people who are intolerant.
“Things of a racist nature are totally unacceptable and football is doing what it can to stamp it out of the game and, fortunately, our club doesn’t suffer from this sort of thing.” The club last night thanked fans for their help in reporting racial abuse to the police.
A police spokeswoman said: “The 25-year-old man was arrested under the Malicious Communications Act. He was subsequently also arrested on suspicion of a racially aggravated public order offence of intentionally causing harassment, alarm or distress.
“The man has now been bailed.”