Balotelli has come in for criticism having scored just one goal for the club since joining from AC Milan for £16m in the summer, but Rodgers is happy with his striker's current work rate.
"I thought he worked very well and very hard," he told reporters. "He maybe thought he wasn't going to play today but you've got to stay with it. You've seen he is working hard and at the moment he is doing his best.
"Unfortunately it's that wee bit of confidence, sometimes when you don't get that goal, that he might lack a little. But he kept going, kept getting into the [right] areas and I thought he and Rickie Lambert worked well when [Lambert] came on.
"I'm a little bit frustrated we didn't win the game but performance-wise I'm happy and our reaction to the midweek game."
Next up for Liverpool is a League Cup encounter against Rodgers's former side Swansea City on Tuesday night.