The fall-out continues to rumble on from the Uruguay international's handball for the second goal in the 2-1 FA Cup win at Mansfield.
Even a Methodist minister from the Nottinghamshire town has waded into the debate, criticising the "evil" of a lack of sportsmanship in football in general.
But Ayre, who dismissed claims by Stags chairman John Radford he was embarrassed by Suarez's actions, said the striker had nothing to worry about.
"There have been plenty of decisions which have gone against Luis this season," he said.
"These things seem to follow Luis around and it's unfortunate, but he has our full support.
"He's a fantastic player who makes a huge contribution to the club.
"Knowing Luis, it won't affect him as he's a very strong character."
On Radford's claims, Ayre added in the Liverpool Echo: "I was surprised when I read his comments because Mansfield's manager and players showed a lot of dignity after the game.
"It's nonsense to say that I was embarrassed."
Suarez's handball prompted Reverend Bob Jones, minister at three Methodist churches in Mansfield, to question the values of the modern game.
"I have long thought that the game of football suffers from two evils, too much money and a lack of sportsmanship," he told the Nottingham Post.
"I watched the game on TV and both my wife and I were incensed.
"On this occasion, the player I believe knew he had done wrong by his reactions following the incident, but felt he either did not want to do the decent thing or felt under too much pressure from what the team and manager's reaction might be.
"I accept the referee made the decision but the player could have been a real gentleman and owned up to it."