Palace host West Ham United on Thursday before making a trip to Southampton for a match on Saturday, and their busy festive period ends with a game at Norwich City four days later.
"I enjoy the training, the matches themselves somewhat less so as I think it's harsh to play at the level we play at with just a day's rest," Hodgson told reporters.
"It's too much to ask. I don't enjoy that part, it's a very dangerous period -- there can be injuries, there can be fatigue. Suddenly you find yourself looking up the table rather than down."
'Can we stop that guy?' - Hodgson annoyed as lawn mower interrupts press conference
Palace, 12th, have a number of senior players sidelined with injury, including defenders Scott Dann, Gary Cahill and Joel Ward, while midfielders Jeffrey Schlupp and Andros Townsend are also out of contention.
"Scott Dann's a strain, and normally they're several weeks," Hodgson added.
"Gary Cahill and others, they're predicting it won't be the coming matches - more like the end of the month if we're lucky. Jeffrey Schlupp and Andros Townsend, it could be even longer.
"Our squad's small. The injuries we picked up -- there were seven going into the weekend."
Nightmare before Christmas for Man Utd as Haaland picks Italian giants - Euro Papers
Time for another row about Man Utd and penalties - The Warm-Up
Palace must find way to thrive without Zaha - Hodgson