The Uruguayan's admission of diving prompted Rodgers to pull him in for another talk, as he is concerned what effect the comments may have on the team - and referees' opinions - for the remainder of the season.
"You normally find players, when their careers are finished, admit to all these kind of things - he just happened to be honest in the middle of his career," said the Reds boss.
"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 (his chat with Suarez) was a clear message."
Rodgers insists the focus which falls on Suarez, and the headlines which follow, is not an issue for his man-management skills.
"He is a real topic of conversation, football and media-wise, and as a manager my responsibility and leadership I have to make comment when I have to," he said.
"It has been quite nice most of this season when it (speculation and criticism) hasn't been about.
"He is tough-minded and, irrespective of what is out there, media-wise he gets on with his job. On the football side there are no complaints.
"I work with Luis every day so I know the character he is. I know he is a good man who wants to do the best for the club."