Although it was a defeat, Rodgers feels the performance of his side was quite positive considering the inexperience of some of the players in his line-up.
"I felt we were too tentative in the first half - but you can understand with young players playing here," he said.
"There wasn't much in the first half but any chances they had were through us giving the ball away.
"I said before we went out that when you play a rival - and this rivalry is massive - you need courage and you need to have belief.
"We wanted to pass the ball, which is great, but it has to be aggressive and we presented them with the ball and three opportunities just by being tentative.
"I am very proud of the fight of the team in the second half having gone 2-0 down.
"Teams who come here often crumble but I thought by the end we deserved something to be honest."