Moyes also said he is concerned about the Uruguayan's tainted history heading into Sunday's fixture against their city rivals at Goodison Park.
The Scot is still uncomfortable about last season's red card given to Jack Rodwell following a challenge on Suarez in the corresponding fixture, claiming that was a result of a dive and a real poor decision by the referee, and the Football Association later rescinded the red card.
When asked if he would be worried about Suarez reputation during the match, Moyes replied: "I would because I think he has got history. I tell you what it will do, it will turn the supporters away from football."
"It is hard for the referees, it really is. But it will turn supporters away from it if they think players are con ning their way to results. People like to see things done correctly, in the main," the Telegraph quoted Moyes, as saying.
"If a ball hits your hand, of course you are going to claim for it. And you will take every decision you get. But when people are out to manufacture it, supporters in general will not like it," he added.
"I don't think there are that many players out there who do it. If I got one, I would be big enough to say, 'would you stay on your feet, please, and stop going down easily'. I would hope I would be big enough to go in and say, 'I don't like that'," he said.
Moyes further said: "Generally. I think it is a discussion to be had. I don't think supporters like the idea of players going down easily. Everybody who has played football and who is involved in it hates to see that happening in the games. Anyone involved in a game would say, 'get up'." (ANI )