The South London club will host Chelsea in their next league fixture following the international break.
"Christian Benteke won't be back for a few weeks, so we still won't have a recognised centre forward," said Hodgson.
"So there are three quality players I can name off the top of my head who could have helped us do a better job against Chelsea.
"But they're not there. So it's got to be the lads I put out there who go out and run their b******s off — if you excuse my expression — to try to do the best job they can possibly do."
Hodgson also admitted that he expects to see fractions in his squad in the coming weeks.
"Obviously, it's going to get more fractious because we put our messages across quite strongly and there will be some players on the field who don't pick up those messages as quickly as others," he said.
"So maybe one or two of those who have picked it up get a bit irritated with one or two who don't pick it up quite as quickly. But that's nothing I can't deal with.
"The mood has been good and the players have been keen to get down to work and try to improve their ability to defend and attack.
"We're a wounded animal in more ways than one — because of the start we've had and the fact we're doing it without five or six very important regular players."