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."