But on Wednesday, Suarez said: "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 [David Moyes] - but the name Suarez sells [papers]."
Rodgers is hoping the admission will not affect officials' opinions of Liverpool and hinder their chances of getting future penalties.
Diving Suarez will be dealt with - Rodgers
The Liverpool boss said: "My main concern is the team. As long as it doesn't affect our chances - we've only had one penalty this year anyway - but as long as it doesn't damage our prospects in the future that is the most important issue.
"Anything that is detrimental towards that is something I don't take too lightly and, if that is something I think affects it, that [chat with Suarez] was a clear message."
Suarez also revealed he felt he was treated harshly following his handball in Liverpool's
2-1 win over Mansfield
earlier this month.
The striker handled the ball before scoring what turned out to be the crucial goal in the FA Cup third-round tie.
"The other day a ball hit my hand with no intention at all, and everybody criticised me because I kissed my wrist," he added.
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