The former England boss took over at Selhurst Park on Tuesday following Frank de Boer's sacking after just four games in charge.
The Dutchman had overseen four straight losses without the team scoring a goal when Palace's owners decided they had seen enough.
Hodgson said on Sky Sports News: "You are looking for character really, you're looking for desire, you're looking for people with enthusiasm and you're looking for people who at least give the impression that they're trying to do what the team wants them to do.
"I think we've got a lot of work to do before I will feel confident that every player fully understands with his role what I'm looking for and what I want him to do. There's more work to do before that happens."
Despite only taking over on Tuesday, Hodgson has been encouraged by what he has seen of his players so far.
"I've seen some signs that the little few things we have done and the one or two things we have said it's not just been completely wasted on them," he said.
"Most importantly of all I refer to those initial qualities - I want to see character, I want to see desire, I want to see enthusiasm, to see a team which shows the fans that they really care."