Suarez was again the centre of attention for all the wrong reasons in the wake of his handball goal that helped the Reds beat non-league Mansfield 2-1 in Sunday's FA Cup third-round tie.
"He has had seven yellow cards this year, but he hasn't warranted all seven," said Rodgers.
"He is a wonderful professional. I think in this country we need to enjoy it whilst he is here because he is a brilliant talent.
"He is a good man as well, a good family man, and as a manager, he is someone who wants to come in and work.
"He wanted to start yesterday's game, even though he has really been my only striker for the last six months.
"Yesterday was a game he was up for because it was street football for him, he enjoys that type of game.
"But I can only talk about his talents. I always try to educate the players, with regard to every aspect of their life.
"As I've said, he's very receptive, and we go forward with him."