The Italy international was suspended for an inappropriate post on social networking site Instagram that was reported to have contained anti-Semitic connotations.
Balotelli pleaded guilty to the charge and manager Rodgers confirmed he will miss Sunday's Premier League match with Arsenal at Anfield because the club do not intend to challenge the ruling.
"We accept the ban," said Rodgers.
"He is here as a football player and is trying to become a better player."
Liverpool welcome Arsene Wenger's men to Anfield looking for another impressive home performance against Arsenal after winning last season's corresponding fixture 5-1.
The Merseyside club are likely to come up against forward Alexis Sanchez, who reportedly turned down a move to Liverpool in the last transfer window.
Rodgers described the former Barcelona man as "world class", but insists the focus is purely on his own team.
"All I know is that he is a world-class player," he added. "He was someone who would have been perfect for us.
"He is an intelligent player and he has great work rate. We know he will be a threat. Arsenal have outstanding players but our focus will be on ourselves."
Rodgers also confirmed that Brad Jones will continue in goal, while centre-back Dejan Lovren faces a late check on a groin injury.
