Suarez admitted to "falling" during October's goalless draw at Anfield in an attempt to win a penalty.
Reds boss Brendan Rodgers on Thursday described diving as "unacceptable" and revealed the club would look to take action.
"I think it is wrong. It is unacceptable. I have spoken to Luis and it will be dealt with internally," he said.
"[Diving] is not something we advocate. Our ethics are correct."
Suarez made the admission to Fox Sports in Argentina, saying: "Football is like that. Sometimes you do things on the field that later you think 'why the hell did I do that?'
"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... I understood that the name Suarez sells (papers)."
No spot-kick was awarded to Suarez, who has previously been derided in England for his perceived theatrics. Following the Anfield match Stoke boss Tony Pulis hit out at the Uruguayan, labelling him "an embarrassment".
Jim Boyce, Britain's representative on FIFA, later described Suarez's dive as "nothing less than cheating", adding that simulation was a "cancer" in the game.
Suarez was back in the spotlight recently following his handball in the build-up to his winning goal against Mansfield in the FA Cup third round.
There were questions as to whether the 25-year-old handled the ball deliberately or if it was accidental.
He said: "The other day a ball hit my hand with no intention at all, and everybody criticised me because I kissed my wrist. Suarez sells.
"That's why they also talk about Suarez having a chat in secret with (Sebastian) Coates in front of (Steven) Gerrard. They make up anything. Everybody should do what they have to do, to talk about football and not anything else."
Suarez also believes foreign players are treated differently in England.
He said: "It's tough. As Carlitos (Carlos Tevez) and Kun (Sergio Aguero) said, the foreigners, and even more the South Americans, receive different treatment than the local ones.
"It's a cultural thing. They have different behaviours. What we have to do is play football, do what we know, what we've always desired. We fought to be here, and suffered a lot to be here. We shouldn't listen to any nonsense they say now."
After speaking with Suarez, Rodgers added: "He has been totally understanding on where I am coming from as manager of the club.
"What was said was wrong, he takes that and we move on."
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