Palace have a tough run of fixtures coming including games against Manchester United, Chelsea and Liverpool in their next four and as it stands they are only out of the bottom three on goal difference.
"It's a cruel blow, but we know what a cruel game football is, so we have to pick ourselves up and try and go again," Hodgson said to 'Sky Sports' after the game.
"At the moment we don't have the fire-power and the players that we would need to go toe-to-toe with these teams.
"We are going to have to try hard and defend well and in depth, work a lot harder in terms of keeping the opposition at bay and hope not to get the dagger thrust at the 88th minute, hoping you would see it through and get a point."