On Tuesday, the East Midlands outfit announced that Shakespeare had been removed from his position in the dugout after just six points were recorded from eight Premier League fixtures.
Appleton has been placed in temporary charge and at his pre-match press conference ahead of the game at Swansea City, the former Oxford United boss revealed that Shakespeare was feeling "a bit raw" about the decision.
The 41-year-old told reporters: "I spoke to him a couple of times. He's a little bit raw still. I don't recall him having lost his job before.
"He's a bit raw but having been there myself I spent a bit of time talking through how I dealt with it etc and I'm sure in the coming days and weeks he'll start thinking positively.
"He's highly respected by all the players and staff at the club. He's been here a long time and done a lot of roles. The one thing I did mention was he was part of me coming here. A top guy."
Shakespeare leaves the King Power Stadium having won 11 of his 26 games in charge of the club.