Gerrard also criticised Phil Neville after the Everton captain was booked for diving in the first half.
In his post-match press conference Moyes said he had spoken to Neville about it and the player himself admitted his actions were wrong.
"With what he said about Luis Suarez before, David Moyes was trying to get in the referee's head, which is fine, that's all part of the game stuff like that," said Gerrard.
"But if that's the case you don't expect your captain to dive like that.
"I think Phil Neville badly let his manager down.
"His manager did every paper, every radio station and every TV channel talking about Luis Suarez and then his captain, who is meant to be setting an example, blatantly dives.
"If David Moyes is a real man and a real manager, which I think he is, then he will be speaking to Phil Neville about his dive."