Benteke goal drought a concern for Hodgson
Benteke hit 15 Premier League goals last season to steer the Eagles away from relegation danger, but has made 12 top-flight appearances without finding the net this term.
The 27-year-old drew another blank in Tuesday's dramatic 2-1 win at home to 10-man Watford, when late goals from Bakary Sako and James McArthur saw Palace snatch all three points after Tom Cleverley's 87th-minute dismissal.
But despite Palace extending their unbeaten run to six league games, Hodgson conceded Benteke's lack of goals is a problem, the striker having missed a late penalty in Saturday's 2-2 draw with Bournemouth after demanding to take the spot-kick.
"Of course, him not scoring is a concern to us, to him and to the fans," Hodgson said at a media conference to preview this weekend's trip to Leicester City. "He needs to keep working hard and make a good contribution to the team.
"We can't afford to carry anyone, let alone a goalscorer who isn't scoring goals. We won't keep reminding him about it. I wouldn't be gaining a great deal by doing that."
RH: "I don't think it's right to talk up or talk down some of the teams around you.
"We have enough pressure and responsibility.
"But if you ask am I pleased with what we have done in the last 10 games, the table does look better." pic.twitter.com/d7Zvhid8Xr
— Crystal Palace F.C. (@CPFC) December 14, 2017
Hodgson accepted the flying Foxes - on a four-game winning streak under new manager Claude Puel - will be a tough test for his recovering side, who sit 18th in the Premier League.
"They're a good team with good players, so the manager has done well since he's come into the club," Hodgson said.
"It's no surprise to us that Leicester are winning matches, scoring goals and playing well because we know what a good team they are. It's not that long ago that they were the champions of England. You don't become champions and lose all your quality within a season.
"Even without the results that they've put together we'd have still been very respectful when we go there on Saturday - and fearing the quality that they have."
Palace will again be without defenders Damien Delaney, Joel Ward and Mamadou Sakho, while defensive midfielder Luka Milivojevic misses out through suspension.
And Hodgson confirmed Palace are unsure when Sakho will be fit to return to action, the ex-Liverpool defender having injured a calf against Bournemouth.
"It's far too early to tell - it's a serious muscle strain or tear," the former England manager added. "Doctors will not put a timescale on it but it's going to be a while, that's for sure."