The controversial forward, who apologized last night for the incident, is facing an FA investigation into his behavior in the match against Chelsea.
But the club has confirmed the player has been fined, and requested that the sum be donated to the campaign group for families of the 1989 disaster which killed 96 of the club's supporters.
"I think he felt like he let a lot of people down yesterday," Ian Ayre, the club's managing director, told Liverpool's website.
"We'll work with Luis - Brendan particularly - on this side of his character in his game. Hopefully that puts the matter to rest from our point of view and we'll wait and see if there's any further action from the football authorities."
Despite the furore surrounding the incident, which saw police being called to speak to Ivanovic after complaints about the bite from members of the public, Ayre looks to have ruled out selling the Uruguayan forward this summer.
"We have to work with him on his discipline - but Luis is a very important player to the club," he said.
"He's a very popular player with his teammates. As we keep saying, he signed a new four-year contract last summer and we'd all love to see him here throughout that contract.
"He's a fantastic player, top scorer and everything we'd want in a striker, so there's no change there. This is more about getting him back on the right track and it's largely down to Brendan now to work with him on that side of his character."
Earlier Ayre had described the player's behaviour as "not befitting of any player wearing a Liverpool shirt".
Suarez looks set to face a Football Association investigation into the incident, which was not seen by referee Kevin Friend but later highlighted by numerous television replays.
The incident occurred when the two players clashed following a challenge in the Chelsea penalty area. Ivanovic complained to referee Kevin Friend that he had been bitten on his right arm by Suarez.
Police are understood to have spoken to the Chelsea defender at the club's training ground after complaints were made, but Ivanovic told officers he did not want to press charges.
Suarez has publicly apologised to Ivanovic after the biting incident which sparked fury in the wake of the dramatic 2-2 draw at Anfield.
"I am deeply sorry for my inexcusable behaviour earlier today during our match against Chelsea," Suarez said in his statement.
"I have issued an apology and have tried to contact Branislav Ivanovic to speak to him personally. I apologise also to my manager, playing colleagues and everyone at Liverpool Football Club for letting them down."
The player later revealed he had spoken to Ivanovic directly by phone to apologise for the incident.
The incident comes just days after Suarez was named on the Professional Footballers Association player of the year shortlist.
It is not the first time Suarez has brought controversy to the club - he was banned for eight matches last season after being found guilty of racially abusing Patrice Evra - and he has previous history of biting.
Immediately before joining the Reds in January 2011 he served a seven-match ban while at Ajax after sinking his teeth into PSV Eindhoven midfielder Otman Bakkal.
Brendan Rodgers, the Liverpool manager, said after the incident "Having reviewed the video footage and spoken to Luis, his behaviour is unacceptable and I have made him aware of this."
Speaking after the match, Rodgers insisted no snap decisions would be taken on the future of the player, who is certain to attract interest from Europe's top clubs after scoring his 30th goal of the season.
"It is not for me to make any rash comments or any predictions now," he added.
"This is a football club where historically players treat people with how the football club respects society, players and everyone.
"There is certainly no one bigger than this football club, as a player or a manager.
"Players are always replaceable now matter how good they think they are. That is how football works.
"Of course there are wonderful talents here we've seen at this club and others over many years.
"You lose a player you think you can't replace but the next one comes along.
"The standards at this football club have been met for many years and that's why it is the worldwide institution that it is.
"The history of this club is about respect and how people are treated and that is something that will always be maintained here and will always be long after I am gone."
Former Liverpool midfielder Jamie Redknapp called what Suarez did "indefensible", coming after the similar incident in Holland.
"He got a seven-game ban at Ajax for doing the same thing," he told Sky Sports.
"He obviously has a real problem. There is that madness-genius gene in him because as a player, you hold your hands up - he's exceptional with people talking about him being player of the year, but what he did today, is indefensible.
"Even the staunchest Liverpool supporters cannot look at that and think that's all right.
"You can't defend that and anyone who tries to is completely wrong, because the club is bigger than any player who has been on the football field.
"What's he doing? Why on earth would you want to take a chunk out of someone's arm when you are on a football field?
"That is an absolutely incredible act of brutality. It's madness."
"He's letting the club down."
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