The Foxes are out of the Europa League after the 2-0 loss at King Power, having secured a goalless draw in the first leg.
They might have dominated possession but Rodgers' side never really looked like threatening Slavia's goal.
And the visitors punished Leicester's apathy when Lukas Provod volleyed in the opener shortly after half-time.
Leicester laboured for an equaliser but were eventually caught down the other end by a fabulous strike from Abdallah Sima with eleven minutes remaining.
"We lost to the better team," said Rodgers. "I take responsibility for the team I've picked. I picked a team I felt could win the game.
"We didn't create enough over two legs. We didn't defend with any intensity. We gave away two disappointing goals. The better team won.
We started pretty well. We didn't have enough quality to break them down.
"I don't want to give too many excuses. [We had] players not available tonight at the top end of the field. However I still expected us to show up more. They'll learn from it.
"We're disappointed to be out but we know we weren't good enough.
"Good luck to Slavia in the next round."