Palace face Arsenal on Sunday.
Hodgson said, "You can't win football matches unless you score goals. Of course it's a concern but the fact is there isn't much more you can about it except keep working, keep trying to create goal chances and hope some of them go in.
"We've not been a team that has spurned many penalty opportunities, for example, but we spurned one the other day. Unfortunately when you get into the type of run that we find ourselves in, that's the sort of thing that happens.
"But the players know what is required, they know they have got the ability and wherewithal to score the goals.
"All we can do until those goals go in is keep trying, and accept that every time we don't score it is going to add to the ballast of games where goals haven't been scored."