O’Shea has been a Spireite for more than four years, scoring 40 goals in almost 200 appearances.
Having told Caldwell last Friday he wanted to move to Bramall Lane, O’Shea got his wishes with a Sheffield United loan spell that will last until the end of the season, when his Chesterfield contract expires.
Evatt paid tribute to the attacking midfielder.
“Jay O’Shea has been a fantastic player for this football club for four of five years,” he said.
“But if he chooses to move on, good luck to him.
“It’s down to the next one to come in fill some big shoes.”
Evatt is of the opinion that players departing is not something he can change, so he’s not going to spend time worrying about the Irishman’s exit.
“All you can do is put your faith in the manager, you can only control the things you can change,” he said.
“It’s down to the manager, I’m sure he has got targets.
“From what I know of Gary Caldwell as a player and what I’ve seen of him so far, he leaves no stone unturned, so I am sure he has targets in mind.”