The Uruguay international found himself in the spotlight again when his theatrical fall in Sunday's goalless draw at Anfield had Stoke manager Tony Pulis calling for three-match bans for those who go to ground too easily.
Reds boss Brendan Rodgers has defended his player and while Suarez has been singled out as the main culprit by recent headlines Ayre believes it would be of greater benefit to consider a wider issue.
"I think it's reputation because of what happened last season," he said.
"I am not surprised by the reaction because we all feel he is a bit of target.
"Now everything Luis Suarez does is in the spotlight.
"But if we are going to treat people because of something they do on the pitch then we should treat everybody equally.
"I am not saying that anyone in particular is targeting him, what I am saying is if there is going to be a debate - whether it's a media debate or other - then it has been to be a fair one about everybody and not about Luis Suarez, which seems to be the case."
Ayre echoed the views of Rodgers by pointing out Suarez has probably been denied more penalties than he has won.
"If you look from the start of this season, or perhaps the end of last season through to last weekend, I think it is fair to say Luis hasn't had the luck of the draw really in terms of decisions," he told Sky Sports News.
"It was proven on many occasions that he was denied what he should have been given - hopefully that changes as the season goes on.
"I just feel his style of play, the way he kind of nips in and out, he's just a target for tackles and defenders if you like.
"The most important thing is it doesn't affect Luis, he just turns it on each week and puts himself out there and he will keep going and that is what we need from him."
Former Juventus forward Alessandro del Piero claims he turned down a summer move to Liverpool out of respect for the victims of the Heysel disaster.
The 37-year-old, who was a free agent after his contract expired with the Italian champions, signed for Sydney FC despite late claims he had been approached about a move to Anfield.
"The negotiations with Sydney were already at an advanced stage and then I thought about what happened at Heysel," Del Piero told Gazzetta dello Sport.
"Juve and Liverpool have worked hard to mend their relationship, but for a lot of people it's something that can never be forgotten."
Suarez admits he needs to improve his behaviour on the pitch and not get so agitated.
The striker, currently in South America preparing for a World Cup qualifier against Argentina, was suspended for last month's defeat by Colombia and then booked for arguing with the referee on his return four days later against Ecuador.
If he gets another yellow card on Friday he will miss Tuesday's game in Bolivia.
"As the years go by you realise what you have to correct," Suarez told El Pais.
"I'm 25 and there are things I must improve, like my attitude on the pitch.
"But that's how I've played since I was a kid. I try to correct it but there are times when my anxiety makes me play that way.
"Everyone knows I gesture a lot, talk and protest, and those are things I must improve on."