The ailing Cottagers went down 3-0 at home to Arsenal and afterwards the newly-installed manager called for an immediate improvement in results if they are to preserve their top-flight status.
Hodgson has lost three and drawn two of the five games he has been in the Craven Cottage hot-seat.
"We have to get to winning matches because the later we leave it, the harder it will become," he said.
"People are realistic but I have to say I don't think the players have given up and if we bring in some new faces, that will improve the spirit even more.
"As far as I'm concerned, it's a work in progress and we're up for that work. We know where we have to improve."