Tony Hibbert and Phil Neville were sent off and Everton also claimed they should have had a late penalty for a foul on Joleon Lescott by Jamie Carragher.
Moyes was heavily critical of referee Mark Clattenburg and also suggested Liverpool skipper Steven Gerrard was implicated in the red card for Hibbert, saying after the match: "The referee pulled out a yellow card and then the Liverpool captain has a word with him and it becomes a red."
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