Liverpool manager Brendan Rodgers insists no one is bigger than the club and Luis Suarez's biting incident will be discussed with the owners.
The Uruguay international scored in the seventh minute of added time - his 30th goal of the season - to snatch a 2-2 draw but his scoring exploits were overshadowed by what went before.
Referee Kevin Friend did not see the incident and despite Ivanovic's protestations took no action.
The 26-year-old rubbed salt into the wound by heading home Daniel Sturridge's cross with virtually the last touch of the match with the clock showing more than the six added minutes.
Rodgers did not want to comment on the incident until he had seen it for himself - declining the opportunity to view an image in his press conference.
But he stressed players had to "accept the consequences" of their actions.
"I hear all sorts of what has supposedly happened but I'll go away, review it and comment later," said Rodgers.
"We'll go away and speak to them (owners Fenway Sports Group) afterwards and take it from there.
"This is a club with incredible values and ethics here. As footballers, managers and staff we are representing this great club on and off the field.
"I will always speak openly and honestly about the players and protect them when I can and if I think they are wrong I will tell them - as I have already happened this season with Luis (when the striker admitted to diving).
"People have to accept it when they do wrong if that's what the case is.
"They have to accept the consequences accordingly. It's disappointing that we are not talking about the football."
Suarez's spell at Anfield, having arrived from Ajax having just served a seven-match suspension for biting PSV Eindhoven midfielder Otman Bakkal, has been dogged by controversy.
Last season he was banned for eight matches after being found guilty of racially abusing Manchester United's Patrice Evra and earlier in the campaign admitted diving in an attempt to win a penalty.
Despite his 'darker' side the striker is still coveted by Europe's top clubs and Liverpool are expected to have to fend off interest from them this summer.
However, Rodgers insisted now was no time to be deciding whether they had to sell him in the wake of the latest incident.
"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 no 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."
Suarez's late goal spoiled what would have been a victorious return to Anfield, almost three years after he left the club, for Chelsea's interim manager Rafael Benitez.
He too claimed not to have seen Suarez's alleged bite and was far more angry about the amount of added time played.
"I thought it was an emotional return," said the Spaniard, whose name was frequently chanted by fans who remember him fondly for the 2005 Champions League triumph.
"I was pleased with the reception of the fans and disappointed with the late goal conceded - especially as I couldn't understand why there were six minutes and 45 seconds (added on).
"It is a strange decision. Some games you have six substitutions and they say three or four minutes but six minutes (had expired) and with a throw-in for us the game was over.
"But six minutes and 45 seconds is difficult to explain. We need to analyse why we didn't stop the cross and they scored but in the normal circumstances we would have finished the game.
"I didn't see the incident that people are asking me about.
"I have not spoken to the players (about Suarez). We were talking about the late goal - it is very frustrating.
"We have plenty of time in the week to speak about it."