The Uruguay international was handed a 10-match suspension by the Football Association for biting the Chelsea defender during Sunday's 2-2 draw with the Blues at Anfield.
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"I am truly sorry about the incident with Branislav Ivanovic," the striker wrote in a statement on Twitter. "I hope that all the people who I have offended at Anfield last Sunday will grant me forgiveness and I again repeat my personal apology to Branislav.
"I know that all the things that are happening to me in England will help me to improve my conduct on the field. Right now, I just want to focus on becoming a better footballer.
"I would like to explain to everybody that I decided to accept the ban because whilst 10 games is clearly greater than those bans given in past cases where players have actually been seriously injured, I acknowledge that my actions were not acceptable on the football pitch so I do not want to give the wrong impression to people by making an appeal.
"I really want to learn from what has happened in the last two-and-a-half years, many things have been said and written about me, I just tried to do my best on the field. I hope to come back early to play."