was quick to apologise via his Twitter account -- but the damage was done as the Uruguayan ended up in hot water and not for the first time in his chequered career.
"I'm sad for what happened this afternoon, I apologize (to) Ivanovic and all (the) football world for my inexcusable behaviour. I'm so sorry about it!!," said the 26-year-old, after the second half incident following a tussle in the penalty area with his club trailing 2-1.
In a statement on Liverpool's official website, Suarez showed further contrition.
"I apologise also to my manager, playing colleagues and everyone at Liverpool Football Club for letting them down," he said after an incident which referee Kevin Friend did not appear to see.
Suarez had earlier been booked for a handball that gifted Chelsea the penalty from which Eden Hazard put the visitors 2-1 up, but he finished the game by heading in a dramatic equaliser in the seventh minute of injury time.
Were it not for the unsavoury incident with Ivanovic his goal would have had Liverpool singing his praises but instead Anfield's hierarchy took a dim view.
Liverpool managing director Ian Ayre noted the player's "unreserved apology" but stated: "His behaviour is not befitting of any player wearing a Liverpool shirt and Luis is aware that he has let himself and everyone associated with the club down. We will deal with the matter internally and await any action from the FA."
Reds' coach Brendan Rodgers said on the club website: "Having reviewed the video footage and spoken to Luis, his behaviour is unacceptable and I have made him aware of this."
Former Liverpool manager Graeme Souness, now a television pundit, said Suarez's future was now in jeopardy.
"He's making it very difficult for himself to stay at Liverpool. That puts him in the last-chance saloon. He is risking everything this great club stands for," said Souness.
Suarez, 26, has regularly hit the headlines since joining Liverpool from Dutch club Ajax two years ago.
Last season he was embroiled in an alleged racist spat with Manchester United defender Patrice Evra
And while with Ajax he was banned for seven games for biting PSV Eindhoven midfielder Otman Bakkal during a Dutch league game in November 2010..
Rodgers did note Liverpool that no one individual player is more important than the club's values.
"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.
"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."
Chelsea had opened the scoring with a near-post header from Oscar in the first half only for Daniel Sturridge to equalise, tapping home Suarez's cross.
Suarez then gave away a penalty with a handball, converted by Eden Hazard, but the striker headed home deep into injury time to rescue a point.
Chelsea manager Rafa Benitez admitted his return to Anfield was "emotional" even though it was overshadowed by the Suarez incident which he said he did not see.
Benitez, who won the European Cup for Liverpool in 2005, was given a rousing reception by the home fans.
"It was an emotional return. I was pleased with the reception of the fans," Benitez said.
"But I was 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 to add the time on. Some games you have six substitutions and they say three or four minutes but six minutes and a throw-in for us the game was over."