The Foxes were defeated by AS Roma in the Europa Conference League semi-final on Thursday night.
The Toffees will be looking to pile more misery on the Foxes in their bid for Premier League survival.
But Rodgers has demanded a response from his troops.
What’s been said
The Leicester boss told BT Sport: "Of course, when you lose the second leg of a semi-final it’s disappointing.
“I thought the atmosphere was absolutely fantastic from both sets of supporters. It was a great arena to come and play in.
“In the second half, we were much better. We imposed ourselves and made changes. In the first half, it wasn’t aggressive enough. The players kept going until the very end but we couldn’t find that big chance. There weren’t many in the game for both teams.
“The corner - it’s been our problem all season. We have tried every structure in the box – man-marking and zonal – but clearly, we lack physicality in the team to deal with certain situations consistently and that has cost us tonight.
“We really dominated the first leg and had opportunities so we always had it in the back of the mind that we might need to change it and get an extra body through the middle. The players responded really well second half.
“It’s been a great journey for us in Europe in the last couple of years. We have a lot of young players that are finding their way and this was a great experience for them.
“That will provide motivation for them next season. We just missed out so we’re disappointed but we need to finish the season strongly now and look to progress in the summer for next season.”