Victory over West Ham on Sunday wasn't enough to keep the Foxes up.
Evans said, "It's difficult for the club and everyone involved. I have no doubt the club will bounce back. The Premier League is where everyone wants to be.
"We played well today but it doesn't mean anything. We had to make sure we won our game and hope the other games went our way but they didn't.
“It's hard to know [why they struggled so much]. The bad start sticks in my mind. It's not easy to turn around. It's hard to win matches. We found it difficult to recover.
“For the last couple of months we said big game, big game every week. But at the end of the day it went down to the final minutes."
On what decisions the club might make, the defender added: “I don't have the answer to that. I'm sure they have a lot of decisions to make. A lot of players are out of contract. There is a lot of talk of players moving on. When there's a relegation that usually happens. There's a lot of decisions for the club to make and I'm sure they'll make the right ones."