Between December 28 and January 2, Palace are scheduled to play Arsenal, Manchester City and Southampton, leaving a minimal amount of time for recovery.
Palace are currently on a six-match unbeaten streak, but Hodgson has already suggested that his team will struggle to cope with the extra demands.
Hodgson told reporters: "I think it's unfortunate if you are a team that gets moved for television and you only get one day rest.
"We have two days between Arsenal and Man City. I find it harsh we only have one day between playing Southampton and Man City. We will find that very hard. Our squad isn't very big."
Despite their improved run of form, Palace remain in the bottom three of the standings.