The Foxes were dumped from the competition in the semi finals after Aston Villa scored a late winner.
The tie ended 3-2 to Villa on aggregate.
But Rodgers chose to look at the positives after the heartbreaking defeat.
"I'm proud of the team, coming into a game like this, of this pressure, for playing with that composure," he told LCFC TV.
"We created enough opportunities to win the tie over both legs, but it wasn't to be.
"It looked like the momentum was with us. Unfortunately just right at the end, we just switched off on our cross, and the guy finishes it at the back post so it's hugely disappointing.
"The scoreboard tells us that they go through, so congratulations to Aston Villa and good luck to them in the final."