Though remaining "disappointed" at the perceived extreme nature of the suspension, the club accept their forward's choice, which he explained in a personal statement on Twitter.
Managing director Ian Ayre wrote: "The charges against Luis were his to consider and we have to respect his decision to not appeal the 10-game ban.
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"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."
Brendan Rodgers, who spoke out against the severity of the ban on Thursday, added: "We can't hide our disappointment at the outcome of this situation but we have to move on and support Luis in his decision.
"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."