Police interviewed the Blackpool striker following the third-round match after a man was ejected by stewards and then detained.
Euell was sitting in the dug-out when the incident happened during Stoke's dramatic 4-3 victory.
Holloway said: "There was one horrible moment when a racist remark was made to Jason by one supporter. I hope the fellow is banned for life.
"We do not want anything like that. Jason is a footballer - it should not matter the colour of his skin. It is disgusting. The stewards believed what Jason said and got him out. I have to thank them for that.
"People around the fellow should have said they were not putting up with what was said. It is wrong. I saw Jason's reaction and tried to calm him down. I thought these days were gone but maybe I am being naive."