Suarez, speaking to a TV station in Argentina, appeared to suggest that he deliberately dived against Stoke City in the game at Anfield earlier this season in a bid to win a penalty.
The player's interview incurred the wrath of his manager Brendan Rodgers, who has said he will be taking internal disciplinary action against the player, but the governing body will not be getting involved.
Suarez was quoted as saying: "I was accused of falling inside the box in a match, and it's true I did it that time, because we were drawing against Stoke at home and we needed anything to win it.
"But after that everybody jumped out to talk - the Stoke coach and the Everton coach - but the name Suarez sells papers."
In response to the comments, Rodgers said: "I think it's wrong. It's unacceptable. I've spoken to Luis and it will be dealt with internally.
"Diving is not something we advocate. Our ethics are correct. He has been totally understanding on where I am coming from as manager of the club.
"This is a big club and, whatever people do say goes around the world, and what was said was wrong and not acceptable. There is no-one bigger than the club or the club's image."