The Reds have come in for criticism in recent weeks for the way they handled Luis Suarez's unsuccessful defence against allegations he racially abused Manchester United's Patrice Evra.
Liverpool were also criticised for allowing their players to wear T-shirts in support of Suarez in last month's game at Wigan.
Then last week there was also an incident in their FA Cup victory at home to Oldham when visiting defender Tom Adeyemi was allegedly racially abused by a fan - for which a man has since been arrested.
The club's reputation has taken a battering in some quarters but Ayre has moved to reaffirm their position on such matters.
"One of the many disappointing things about recent events is that it has led some people to the perception that Liverpool Football Club's stance on racism and discrimination is not as firm as it is," he said.
"That is sad for the many fantastic people who work for this club and for our community team."
He told BBC Sport: "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."
On the Adeyemi issue he added in the club's programme: "It is important to us all here that nobody is left in any doubt as to where Liverpool Football Club stand on this.
"Such behaviour will not be tolerated."
In the wake of the backlash they received for their approach to Suarez's defence Ayre fully expects the Uruguay international to be the target of abuse from opposition fans.
Suarez has already served half of his eight-match ban after being found guilty of racially abusing Evra and, coincidentally, his first away match is likely to be at Old Trafford where he is likely to be afforded the most hostile of welcomes.
"It will be tough, we shouldn't kid ourselves that opposing fans are going to give him the best of times because that's the nature of football," Ayre told BBC Sport.
"But he will get 100% support from Liverpool Football Club.
"Luis has come in for a lot of criticism but, we made a decision, Luis made a decision, not to appeal and the reason we did that was to move on.
"He also made a decision not to appeal the ban. Those things have been accepted and he is serving the penalty so we start afresh.
"The best way Luis can come back is to get on the pitch and score some goals and that's what everyone will expect of him."