Respective knee and ankle injuries suffered by Jeffrey Schlupp and Andros Townsend mean they will be absent for what their manager described as "months, and closer to one month" when other influential players are also absent.
Hodgson has long spoken of his priorities being to recruit a goalkeeper and striker, but before Townsend and Schlupp, he had already also lost Joel Ward, Scott Dann, Mamadou Sakho, Ruben-Loftus-Cheek and Jason Puncheon to injury.
That Connor Wickham was a long-term absentee prior to his appointment means Palace are without almost an entire Premier League starting XI, and Hodgson said: "We are not having many transfers confirmed in this window.
"I know that (Francis) Coquelin has gone to Valencia, for example, that (Virgil) van Dijk has gone to Liverpool; I think (Alex) Pritchard has gone to Huddersfield.
"But we are not exactly reading every day that this player has been signed, that player has been signed. The one thing we know for certain is that the agents out there are working 24-7 and the clubs, many like ourselves, are working very hard to find an answer to areas to where we need reinforcements.
"It is interesting to see that very few transfers seem to have been actually nailed down in the middle of January.
"It is going to be a busy month, that is for sure. What actually happens at the end of it in terms of what players arrive here - if any - is another question altogether.
"I have sketched out the profiles, we have identified the areas where we would like some players to come in. Big question, are we going to find them? That is not just Crystal Palace asking that question, it is probably everyone from the top three or four downwards."
Palace host Burnley on Saturday at Selhurst Park, but on Thursday Hodgson had a meeting of similar significance with the club's American owners. Josh Harris and David Blitzer were in London for the Boston Celtics' 114-103 NBA victory over Philadelphia 76ers, who they also own, and Hodgson said: "They were here (at the Palace training ground).
"They spoke to the sports science department. I wasn't a party to that discussion but it would have been an interesting one.
"I had a long time talking to (Harris) and David Blitzer and Steve Parish about the future of the club and our plans and our hopes.
"Again, like us, they are aware of the situation and they want to help (in the transfer market), and I am sure they will do their very best to help. But it is one thing wanting to help and another thing trying to find the ways of helping."