Palace have failed to win since and are stuck on four points after 11 league games, including nine defeats.
"We need points and I'd have settled for playing much worse and having a bit of good fortune, such as a ball deflecting past a goalkeeper or the referee awarding a penalty which isn't," Hodgson said.
"When we look at the table we're still on four points and we're getting further away from the teams that are just outside of the relegation zone, and our task gets harder with every defeat.
"It would be nice by the end of the season to have one person who is a centre-forward and goalscorer."
Striker Christian Benteke, Palace's leading scorer last season, has been out since September due to a knee injury and the club have suffered in the Belgian's absence, scoring just four league goals.
Palace host 15th-placed Everton after the international break on Nov. 18.
(Reporting by Aditi Prakash in Bengaluru, editing by Ed Osmond)
