Liverpool striker Sturridge has returned to Anfield due to a thigh problem while Hodgson revealed Cardiff defender Caulker had turned his ankle in training.
Both are expected to enter contention for Tuesday's game in Ukraine but Hodgson was reticent over Sturridge's involvement.
He told Sky Sports News: "We've not exactly been lucky have we? Now there's Daniel and there was Wayne (Rooney) and two potential right-backs in Glen Johnson and Phil Jones, and before that Alex Oxlade-Chamberlain.
"So we have lost five players and a few weeks ago I was really banking on them.
"It's a great opportunity for the ones who maybe wouldn't have got a game had they been available.
"(Sturridge) has worked hard at his treatment and the initial prognosis was that he wouldn't be fit for either of them but he didn't accept that.
"He's worked very hard and had the necessary treatment but I think it will be touch and go.
"On Sunday evening we'll have a training session before heading for Ukraine. If he passes it then he'll be with us, otherwise then he'll be staying with Liverpool."
Referring to Caulker, he added: "Unfortunately, in training he turned his ankle. It's not a serious matter but it will keep him out of the game.
"It won't keep him out of the Ukraine game, he's expected to do some running, but he won't be on the bench."