Rodgers' men almost took all three points in Sunday's game with Raheem Sterling hitting the crossbar after Jose Enrique had a goal disallowed for offside.
"I thought there was a marked difference," said Rodgers.
"I was really pleased with the quality of our game today, I thought our build-up play was good and we got through the thirds well.
"I just thought we needed a fraction more belief in the final third. There were opportunities around the box where we could have got a shot off a bit quicker.
"That comes from certain types of player and personnel you have in.
"I thought the method in our game was good, and people who would have seen the game at the end of last season would have seen a difference today, hopefully.
"We were unfortunate with the offside goal that was ruled out. I thought that was a goal having seen the replays of it.
"I'll never say coming here is two points dropped because it's a difficult place to come. Our performance level is continually improving. We're just chipping away at climbing up the league, and we'll do that."
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