The ex-player was fined £1,000 after he admitted using “threatening or abusive words or behaviour”.
Gascoigne, 49, asked Errol Rowe “can you smile please, because I can’t see you?”
District Judge Graham Wilkinson also ordered Gascoigne to pay Mr Rowe £1,000 in compensation.
Mr Wilkinson told Gascoigne “You sought to get a laugh from an audience of over 1,000 people because of the colour of Mr Rowe’s skin.”
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He praised the Crown Prosecution Service for taking the case to court, saying Gascoigne’s comment at Wolverhampton Civic Hall on 30 November was an example of “insidious” racism which needed to be challenged.
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The judge told Gascoigne: “Mr Rowe was clearly humiliated on stage, as part of an act.
“As a society it is important that we challenge racially-aggravated behaviour in all its forms.
“It is the creeping ‘low-level’ racism that society still needs to challenge.
“A message needs to be sent that in the 21st century society that we live in, such action, such words will not be tolerated.
“It is not acceptable to laugh words like this off as some form of joke.”
He told Gascoigne what happened was a “stain on his character”.
Gascoigne, whose career included spells at Newcastle United, Tottenham Hotspur and Rangers, changed his plea to guilty before the first witness was called to give evidence.
On his way into court, the retired star stopped to sign autographs, including on a man’s chest.