"It should have been a win for ourselves, I thought we played terrific and were the dominant team," Rodgers told BBC Sport. "We scored two wonderful goals and I am disappointed with the goals we conceded.
"The template of our game is improving, we need to cut out the mistakes and we can challenge at top of the league.
"We have come to the home of the champions and dominated. We know we can be better."
The result means that Liverpool stay in seventh place in the table.