Rodgers was pleased with Barnes' goalscoring contribution after the Academy graduate netted his second strike in three games in all competitions.
He said: “The important thing for us was getting back to creating the opportunities. We had a lot of good creativity today.
“Harvey [Barnes], I was delighted with. It's important that the front players help Jamie [Vardy] in terms of goalscoring, so I thought there was a greater threat with him and Ayo (Ayoze Pérez) today.
“He took his goal really, really well and gave us a good start in the game. Burnley are very good on set-pieces, so sometimes you will concede.
“He gets a good run, Ben Mee, and we just didn't deal well with the second ball. Then, we obviously have other opportunities, including the penalty, to get in front.
“It's just one of those days for us. It's easy to analyse, but now we have to go away and look to get our three points, but also a performance, on Wednesday."