The Italy man opened his account for the club in their thrilling 2-1 UEFA Champions League win over Ludogorets on Tuesday.
Balotelli shrugged off the attentions of his marker to put Liverpool ahead after 82 minutes of frustration for the Anfield faithful.
Dani Abalo struck what looked to be a stunning equaliser in the first minute of stoppage time, but an error from debutant goalkeeper Milan Borjan resulted in the Canadian fouling Javier Manquillo in the penalty area and Steven Gerrard held his nerve to secure victory from the spot in the 93rd minute.
Balotelli led the line in the absence of injured strike partner Daniel Sturridge, but Rodgers said he hopes a first goal in Liverpool colours will inspire the former Manchester City man to better things, with Sturridge set to return in two weeks' time.
Rodgers said: "He's used to scoring. He'd already mentioned he'd had two games and hadn't scored.
"I just feel he needs to be in the box more. Because of his link-up play, he drops in.
"I said to him at half-time 'just make sure when the ball is in wide areas you're penalty spot in, rather than penalty spot out'.
"He finds himself pulling back outside the box for the cut-back a lot of the time.
"He's six foot three and great in the air. When the cross came in, he showed great physical strength, a touch, and then the finish was a brilliant one. It was wonderful technique with the outside of his foot. It'll give him a whole load of confidence.
"On top of that I thought he worked very hard - he worked and was pressing. He's still adapting and still trying to get fit because he's been behind the others in pre-season.
"He showed his quality and that got us the goal."
