The 20-year-old attacker started the campaign in fine form with three goals in his opening five Premier League matches.
Sterling has failed to replicate those early-season performances in recent matches, though, while rumours he refused to sign a new contract worth an estimated £70,000 a week also drew criticism.
However, Rodgers has leapt to the defence of the England international and stated that his showing in Wednesday's 3-1 League Cup win at Bournemouth - in which he scored twice - is proof of his importance to the team.
"As I've said before he's an outstanding talent, he's been great for us," Rodgers said.
"It's been incredible the stick that the kid has received - people trying to criticise him and put the focus on to him.
"He's been outstanding for us and it was another great performance from him the other night in another difficult game."
Sterling has been employed in a more central attacking role in Liverpool's last two matches and Rodgers is pondering whether to do the same in Sunday's Premier League encounter with Arsenal at Anfield.
"The kid has been fantastic where ever he's played this season," he added.
"Outstanding the other night. We'll just see what's in the best interests of the team."
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