The club and its American ownership backed Suarez after the racist-abuse verdict, hitting out at the English Football Association process.
After Suarez sunk his teeth into Ivanovic during a Premier League game in April, Liverpool immediately condemned the player's actions, while still claiming he was being victimized with his hefty sanction.
But Liverpool, whose principal owner is sports tycoon John Henry, has learnt lessons from how it handled the Suarez cases.
"What's important at those times is to ensure we act respectively and professionally as a football club, and in the past we've got some of that wrong and more recently we got that right," Ayre said.
"We have a process now," he added. "It's not a Luis Suarez process — it's a process for any crisis whether it's on the pitch or off the pitch."
For now, Suarez is back helping Liverpool's bid to return to the top four and qualify for the Champions League again.
"I'm here to help the team and help Liverpool and I'll try my best," Suarez said after the game at Old Trafford.
And Ayre was glad to see him back "terrorizing defenders."
"He is a great team member," Ayre said. "The players are supportive of him and he is supportive of them. The most important thing is that he is on the football pitch, and most importantly committed to playing for Liverpool.
Rob Harris can be followed at www.twitter.com/RobHarris
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