The club let go of Cooper after only 12 Premier League games, with Enzo Maresca having got them up from the Championship last season.
After Maresca left for Chelsea, Cooper came in to manage the Foxes at the King Power Stadium.
Asked about Cooper during a press conference on Friday, Dawson said: “It’s a little bit unexpected in terms of the news. I’ve had a few messages back and forth with Steve to check he’s okay. It’s never nice when three good players lose their jobs.
“Then the focus has very quickly shifted onto getting back in with the players, preparing training and looking forward to the game. It’s been a whirlwind, as you can imagine.
“The players shared some of that unexpectedness earlier in the week. There'll be quite a lot of them in the group who have been in similar situations before where a manager has lost his job and they know that’s the time when all eyes are on them. They’ve been professional and worked well.”
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