Rodgers noted an improvement in his side's performance, but was frustrated with the two goals they conceded against the Clarets.
“It's an easy game to analyse and dissect," Rodgers told LCFC TV. “I think that we were the better team, we had a host of chances to win the game and played reasonably well in terms of the performance, but it's a mix of their goalkeeper (Nick Pope) making some fantastic saves and us missing good opportunities.
“Then, I suppose the biggest disappointment is the second goal because I would expect my midfield players to track runs into the box and [Ashley] Westwood had a greater desire to score than what we did to stop it.
"That's the big disappointment for us, that if you win games, you have to earn that right. Like I say, we played better today. We were more dynamic in our game and created opportunities, but we have to be better."