Former Foxes striker Chris Wood was among the scorers, moments before Jamie Vardy saw a penalty saved by Burnley keeper Nick Pope.
Ashley Westwood grabbed the decisive goal towards the end to take all the points away from the Foxes.
However, Rodgers believed Leicester created enough danger to have won the game.
“We were clearly the better team,” he told BBC Sport. “We created a host of opportunities but didn’t take them.
“We tried to get an extra striker in but it wasn’t to be for us.
“We looked dangerous throughout the game, to come away with nothing is disappointing.
“At 1-1 I still believed we would create enough chances to win the game. But Burnley at set-pieces are notorious. Everyone knows how strong they are.
“We could have defended it better though. The second goal is the real disappointment, we didn’t do the basics well.”
Rodgers had to work without two of his young English talents, with Ben Chilwell and Hamza Choudhury both missing out of the squad, something that didn’t aid Leicester’s online betting odds with Bovada prior to kick off – and the Leicester boss revealed why.
“They weren’t available for key sessions in the week. Ben’s obviously been a bit tired anyway of late. He’s played a lot of games lately.
“They both missed an important session though, and that’s why they’re not in the squad.”
With Leicester missing their chance to go level on points with Manchester City, after they also slipped up this weekend, Rodgers fended off questions that his side would be lacking confidence ahead of their clash with West Ham on Wednesday.
“We go into every game with a confidence and an ambition to play well and win.
“We had a great start to the season. Now we’ve got fifteen games to go and we have to re-focus and get our winning mentality back again. That’s fighting, that’s running.”
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