The duo were both on target as England cruised to a comfortable victory that sees them maintain their 100 per cent Euro 2016 qualifying record.
Next up for the Three Lions is a friendly in Turin but Hodgson says he expects Welbeck to join Sterling in missing the game.
"It's two blows in a way because I've always known Raheem Sterling has been waiting for an injection in his toe - he has been playing through an injury for a while now," he told ITV Sport.
"He does ever so well when he does play through it but I've always known that he needed this injection.
"I agreed with he and Brendan that he would play tonight's game which is of course the qualifier, but that he would have the injection.
"If we're unlucky we're going to lose him and Welbeck, which is a blow for us, not only because they played well tonight but because they're an important part of a system that we're trying to play.
Welbeck is struggling with a knee problem and while Hodgson insisted it was not a serious injury, he does feel the Arsenal man may not be quite ready to face Antonio Conte's men.
"Welbeck’s injury towards the end of the game which will probably keep him out of Tuesday’s game, it’s a little bit unfortunate for a game that means a lot to us going back to Italy that we are going to be short of a few players," he told reporters.
"It’s a tweak to the knee, he’s being assessed by the medical staff now. We won’t get a clear idea until tomorrow. The medical staff have given me the impression they aren’t terribly worried but Tuesday may be too soon."
Hodgson also confirmed that James Milner and Leighton Baines would also be returning to their clubs for treatment with Ryan Bertrand set to be called up for the Italy game.