The Foxes went ahead on the 33rd minute mark through Harvey Barnes, but the hosts got their equalizer from Chris Wood 11 minutes after the break.
Jamie Vardy had the chance to give Rodgers’ men the lead from the penalty spot, unfortunately his effort was saved by Nick Pope.
Ashley Westwood’s late strike secured the maximum points for the Clarets, who were winless in their last four league games.
Rodgers said the visitors were clearly the better side as the statistics shows, but luck however eluded them.
"It's an easy game to analyse,” the former Liverpool and Celtic coach told Sky Sports.
“We were clearly the better team, took the lead and created a lot of chances. But it was down to their goalkeeper having a good game and us missing opportunities.”
"And then for the (second) goal we conceded, Westwood has run off our midfield, and that's the basics you have to get right in football.”
“So if you are not going to win the game you have to do the dirty work and his (Westwood's) desire to score was greater than our desire to defend.”
"I think we started the second half well, we were the dominant team and looked dangerous.”
“They are very good on set pieces so sometimes that can happen. But of course from that we still got chances to score.”
“Unfortunately in wasn't to be, it's disappointing but we have to move on now and get ready for Wednesday."
