The Liverpool striker told the Football Association on Friday he would accept the ban for attacking Chelsea defender Branislav Ivanovic at Anfield last Sunday.
A follow-up statement from Suarez, released on his Facebook page, pointed to a perceived inconsistency between his punishment and those in "past cases where players have actually been seriously injured".
But the Uruguay international struck a contrite tone overall, saying: "I hope all the people I have offended will grant me forgiveness and I repeat my personal apology to Branislav.
"I know all the things happening to me in England will help me improve my conduct on the field.
"I decided to accept the ban because, whilst 10 games is clearly greater than bans given in past cases where players have actually been seriously injured, I acknowledge that my actions were not acceptable. I do not want to give the wrong impression to people by making an appeal."
Suarez, who was banned for eight games last season for racially abusing Manchester United's Patrice Evra, will not be seen again in the Premier League until the end of September.
His statement went on: "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."
Liverpool's managing director Ian Ayre said: "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."
Brendan Rodgers said: "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, but we will have the opportunity to welcome a better person and player when he returns."