Everton manager David Moyes was furious with the England captain, and with referee Mark Clattenburg for a series of decisions that reduced the hosts to nine men and allowed Dirk Kuyt, only booked for a dreadful tackle, to score two second-half penalties in Liverpool's 2-1 victory.
Moyes was convinced Gerrard had influenced the referee into giving Hibbert a red card after the Everton defender had brought him down in the box for the equalising penalty in the 54th minute.
'The referee pulled out a yellow card for Tony Hibbert and not a red one until the captain [Gerrard] went over and spoke to him, so maybe he has changed his mind,' said an angry Moyes. 'I think the penalty kick itself was debatable. Ours in the last minute was not debatable.'
In a clear barb at Clattenburg, Moyes added: 'The truth is if you didn't see it, maybe you shouldn't be out there doing the job.'
Everton also argued that Kuyt should not have been on the field to score his goals after a crazy 'kung fu' lunge at Phil Neville produced only a caution.
And the home side were visibly incensed when they were not awarded a penalty themselves in the final seconds after Jamie Carragher wrestled Joleon Lescott to the ground.
Liverpool manager Rafa Benitez, relieved to end a run of three successive draws in the Premier League, backed Clattenburg's decisions and controversially claimed Lescott had dived for his late penalty appeal.
'In England you don't like to see players diving,' said Benitez, who joined his players as they gathered in front of the Liverpool fans to celebrate after the final whistle. But Benitez's accusation brought an angry retort from Moyes.
He said: 'It was not a dive, that is for sure. I think Joleon Lescott would probably be the last person to dive. I think he was just too strong for Carragher and Jamie had to pull him to the ground.'
To complete Everton's sense of injustice, it was Kuyt who scored again from the spot after Neville handled a shot by substitute Lucas and was shown a red card.
Everton felt Kuyt should have been ordered off for his foul on Neville in the 63rd minute.
Moyes said: 'We had a directive that a two-footed tackle off the ground was a sending-off offence. There was four feet of space below Kuyt when he jumped off the ground two-footed. And he goes on to score the winning goal.'
Benitez, whose priority is to lead Liverpool to their first title since 1990, sprang a surprise by taking off Gerrard after 72 minutes.
He said: 'We needed to play with our heads and not our hearts.'