Cole had one his better games in a Reds shirt, scoring his first goal for the club since April 2011.
"Joe Cole gave everything. It was a terrific pass to Suso early in the game to set up the first goal and he gets his finish for the second. There was a number of positives," said Rodgers.
"I think he is still not 100% but he came in and was much better in his offensive part of his game.
"He was clever and bright in between people and that is the nature of those guys at the top end of the field: they have to create goals and score goals."