The Uruguayan is currently serving an eight-match suspension after the Reds decided against appealing the FA sanction imposed when he was found guilty of racially abusing Manchester United defender Patrice Evra.
Liverpool have also been caught up in further controversy after the club's fans allegedly racially taunted Oldham Athletic's Tom Adeyemi during a recent FA Cup clash, and Ayre concedes that it has been a "difficult time" for the Anfield outfit.
"The perception of how we are or have been over the past few weeks is not how we want it," he told the BBC.
"It has been a difficult time for everyone at the club. The key for us is that this club want to fight racism and discrimination."
Suarez will be available for selection again when Kenny Dalglish's side face Tottenham on February 6, although Ayre expects he will be in for a tough time from opposition fans for the rest of the campaign.
"It has been a difficult period but we will get through it," he added.
"It will be tough, we shouldn't kid ourselves that opposing fans are going to give him [Suarez] the best of times. We made a decision, Luis made a decision, not to appeal and the reason we did that was to move on.
"The best way he can come back is to get on the pitch and score some goals, and that's what everyone will expect of him."
Dalglish, meanwhile, reflected on the investigation surrounding the alleged abuse of Adeyemi in his programme notes prior to Liverpool's 0-0 draw with Stoke City and insists the club are "deeply sorry for what happened".
"Whatever the outcome of that investigation, we are deeply sorry for what happened," he wrote.
"We do not want and will not tolerate racism or discrimination anywhere near football, and certainly not anywhere near this football club. The club is blessed with a worldwide fan base, made up of different nationalities and diverse cultures, all of whom come together as part of the Liverpool family.
"The club will continue its proud record of fighting all forms of discrimination.
"Past, present or future, it has no place at Anfield, in our club or in the game.
"We will give any help we can to Tom, Oldham Athletic and the police to ensure this incident is dealt with properly."
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