Zaha will miss this weekend's game with Leicester, and the 'Eagles' have not won a game without the forward since September 2016.
"All curses have to be lifted in some ways, there's only one way we can lift the curse and that's if we win the game," the former England manager said.
"So we have another opportunity. It is a fact and it will be a fact and I'll have to consistently answer the question until such time we play a game with him unable to play and we win."
When asked if the run could now be playing on his player's minds, Hodgson said: "It depends how much they read and take in, as far as we're concerned it doesn't get mentioned.
"If Wilf's playing we work on the team with him in, if not then we train other ways. We don't live in a bubble, so we do see it. I can't sit here and say it makes no difference to us and has no affect on us.
"The one thing you can always do if you're given the chance to put on the shirt is to go out there and play a fantastic game. Nobody can stop Jordan Ayew going out and scoring a hat-trick tomorrow except Leicester City."