Palace have lifted themselves out of the mire since Hodgson's arrival at the club last September with last Saturday's [13 January] victory over Burnley seeing them rise into 12th in the Premier League – five points clear of the drop zone.
But injuries are beginning to take their toll with Scott Dann and Jason Puncheon out for the rest of the season with Ruben Loftus-Cheek now ruled out until further notice. Christian Benteke's struggles in front of goal – the Belgium international has scored once in 17 appearances this term – also present a problem for the manager.
The Eagles face a trip to Arsenal on Saturday – with the Gunners hoping to have a deal for Manchester United's Henrikh Mkhitaryan pushed through in time for him to feature. With less than two weeks of the January transfer window remaining, Hodgson insists four new faces are still a realistic prospect, with injuries to the likes of Chelsea loanee Loftus-Cheek and Jeffrey Schlupp forcing their hand somewhat.
"Our realistic thoughts after I'd been in the club two or three weeks was four, to make the squad as balanced and well-covered as it could be," Hodgson told a press conference on Thursday.
"The reason I said it could go higher than that is quite simply because we've lost two players until the end of the season, Jeffrey Schlupp is likely to be out for quite a while and we are uncertain at the moment as to how long Ruben Loftus-Cheek will be out.
"There are four players there that I really counted on as being part of our first XI even that we've lost.
"I don't think it's unrealistic to think if we could get more than four players, it would be good for us, if we don't get the four players then our squad is going to be short of numbers apart from anything else.
"We are certainly going to be weak in certain areas where we don't have the cover and the competition for places we would like, but we are also actually going to be short of numbers."
Palace suffered a 3-2 defeat when they hosted Arsenal at Selhurst Park just after Christmas, with Alexis Sanchez scoring twice that evening. Those could turn out to be his last goals for the club, with a move to Manchester United now edging ever closer.