The premier says that the younger generation are liable to copy the behaviour of professional footballers, and has backed the Football Association's 10-game punishment
The Uruguayan bit Chelsea's Branislav Ivanovic during the 2-2 draw at Anfield on Sunday, and has been banned for 10 matches by the Football Association.
And speaking to BBC Breakfast, Cameron stated that incidents like this deserve to be severely punished by the governing body.
SUAREZ BANNED FOR 10 GAMES
Luis Suarez is 11/8 with Paddy Power to never play for Liverpool again
"I've got a seven-year-old son who just loves watching football and when players behave like this it just sets the most appalling example to young people in our country.
"That's up to the FA, it's not my decision. The FA makes the decision, it is entirely independent and that is the way it should work.
"I'm going to leave it entirely to the FA. But if you're asking me as a dad and as a human being, do I think we should have tough penalties when players behave like this.
"There are people, I've read in some newspapers, who think somehow this isn't serious. I think it is serious, when we're trying to bring up our children properly, they do see football players as role models.
"Bringing up children is one of the toughest things we do but you can't wrap them in cotton wool and hide them away from the world, they do see these real-life examples and they repeat them back to you."
Meanwhile, former England rugby union international Austin Healey has said that Suarez got off lightly.
"10 game ban for #suarez is unfair should of been 20.. shocking role model for kids.. if you support him ur luv of talent has blinded you," he tweeted.
"Point is the FA are not strong enough in protecting the image of the game.. clubs and players have way too much power.. sports image at risk."
Liverpool and Suarez have until 12:00BST on Friday to appeal the decision, or he will miss the rest of the current campaign and the first six matches of next season.