The Uruguay international has revealed that he wants to learn from his past mistakes and improve his conduct on the field following his decision not to appeal the suspension for biting Chelsea defender Branislav Ivanovic.
"We can't hide our disappointment at the outcome of this situation, but we have to move on and support Luis in his decision," Rodgers told the club's official website.
"Luis has made a huge contribution to the squad this season and we respect his decision to accept the ban. He will be missed for the remainder of this season and the early part of next, but we will have the opportunity to welcome a better person and player when he returns."
Managing director Ian Ayre added: "The charges against Luis were his to consider and we have to respect his decision to not appeal the 10-game ban. We are all disappointed at the severity of the punishment and in particular the differing standards that have been applied across various previous incidents.
"Luis is an important member of our team and nothing has changed in that regard. We are committed to helping him improve his conduct and he will be given our full support. We look forward to him returning to the team next season when he is available for selection."
Suarez will be absent for the Reds' last four Premier League games of the campaign and the first six of next season.