The original incident involving Suarez and Manchester United's Patrice Evra was followed by the Merseyside players and manager wearing shirts supporting the Uruguayan, a gesture that drew widespread criticism.
The problem was further exacerbated when a Liverpool fan was arrested for alleged racial abuse following the FA Cup win over Oldham.
However, suggestions that the club are not interested in campaigns to rid football of racism have been rubbished by Ayre.
"There has been a perception the club isn't doing what it should be doing," said the managing director.
"The players showed support for Luis, which was fantastic. But then some people interpreted that wrongly as the players saying they're not interested in the fight against racism.
"That is totally and utterly rubbish."
Suarez will serve the fifth of his eight-match ban when Liverpool face Stoke this afternoon.