The Italian, who had a Liver bird sculpted into his hair for the occasion, is yet to score a Barclays Premier League goal for the Reds and could not take advantage of a number of decent opportunities.
Balotelli should have made it 2-0 moments after Steven Gerrard opened the scoring but he hit the bar from close range and Everton went on to secure a 1-1 draw through Phil Jagielka's stunning late strike.
Balotelli has a reputation as a hot-head and was the target of a number of robust challenges but did not react and was heavily involved in the game.
Rodgers said: "He needs to focus on the game and I made that point beforehand. This is a game where emotions are high and it can be difficult. But you're going to be in with a greater chance to win as long as you've got 11 players on the field
"And I think overall in his time here he's responded very, very well. I thought his work-rate was excellent. His pressure, his physique at the top end of the field for us was very good and he looked like he could get a goal
"I was disappointed he didn't score but, as long as he's working well and working hard, he will get goals."
There were a number of impressive Liverpool performers, with Alberto Moreno, Gerrard, Jordan Henderon and Raheem Sterling all standing out along with boyhood Everton fan Adam Lallana
The midfielder was also making his Merseyside derby debut and would have opened the scoring early on but for a fine save from Tim Howard
Lallana was a constant thorn in Everton's side, and Rodgers said: " I thought he was outstanding.
"To come into his first derby game and play with that quality and that intensity
And he played the whole game during the week against Middlesbrough, penalties and all, so to deliver that performance was great because it shows he's getting fitter and fitter with each game."
Source: PA