The loss for Palace saw them stay in the drop zone ahead of Saturday's trip to Chelsea.
But defiant Hodgson - still with nine players injured - has refused to throw in the towel. He said: “We're in the relegation zone. After seven games everyone told me we were relegated.
“At the moment we are in the zone, but not relegated. We were eight points adrift, and now we're one point adrift. I don't need convincing that the team has qualities.
“The team has determination and enormous fighting spirit. Who knows? Maybe some of these last minute goals and fortunate moments will eventually fall our way as the season unfolds.
“If we can get some of the players of quality and experience who are currently in the treatment room back on the field, who knows? It would certainly hope the senior players who are doing a wonderful job at the moment in their efforts."