While Poyet has insisted that Suarez's actions were wrong, he believes that there are double standards within the English game when it comes to the striker.
"We exaggerate too much," Poyet told The Times. "Luis knows what he has done, he knows he shouldn't do it and it would be better for him, of course, not to have any more issues this year.
"There are players who have done terrible things and apologised after two minutes and been portrayed as being as a hero for apologising so quickly.
"Luis Suarez apologises and nobody believes the apology. It's sad. Are they living their lives by the same rules? I don't like that. There is plenty of hypocrisy in football now."
The Uruguayan boss also believes that the severity of the incident, which Suarez has apologised for, should be put into perspective with regards to other on-field clashes.
"He tried to bite someone on the arm - no harm really," Poyet added. "A little pain. But if a player goes over the top of the ball and tries to break a leg? That's good because we are strong and we like the tackle.
"That's where we are in England. I know where I am living, and I adapt and I live with it. I would take him somewhere else, to another country."
Meanwhile, Liverpool have reiterated that they want Suarez to see out the rest of his contract at Anfield.