Ian Hardley made a highly offensive comment towards a PC at the Birmingham and Millwall fixture in April last year.
The 60-year-old from Kent was charged with a public order offence causing harassment, alarm or distress.
He pleaded guilty at Birmingham Magistrates' Court on Monday and was given a football banning order for four years.
He was also ordered to pay a total of £519 incorporating a fine, court costs and compensation.
There is no place for discrimination in football, or society in general, and we'll seek to bring those involved before the courts to face punishment.