The 53-year-old was popular with the players and part of Ranieri's staff during Leicester's surprise title win two seasons ago, but paid the price for a poor start that has left the team third-bottom of the table.
"I think the initial feeling was of surprise, but having spoken to (the players) today they are obviously still raw," Appleton told a news conference on Thursday.
"They have lost a manager they obviously respected highly and liked as a person, not just as a manager and a coach. I'm hoping they don't need lifting.
"The group is positive. I fully expect to come in tomorrow and have a mindset that is focused simply on what is needed for Saturday."
Appleton, who described Shakespeare as "a top guy", said he was surprised by the sacking but concentrating on picking the best team to face Swansea at the Liberty Stadium.
"I spoke to (Shakespeare) a couple of times," he added. "He's a little bit raw still. I don't recall him having lost his job before... I'm sure in the coming days and weeks he'll start thinking positively."
Swansea manager Paul Clement, whose side are 13th but just two points better off than Leicester, warned his players they could face a backlash from the Foxes.
"What will their reaction be to the news?" Clement said. "We have to be ready for a potential backlash or an upturn in form... We have to expect a reaction, they are professionals and will want to win, whoever is in charge. I am sure of it."
Swansea striker Wilfried Bony is out with a hamstring injury but is expected back in training next week, while midfielder Renato Sanches is available after missing last week's 2-0 win over Huddersfield.
Midfielder Leroy Fer is suspended for the game after picking up his fifth yellow card of the season.
(Writing by Simon Jennings in Bengaluru; Editing by Christian Radnedge)
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