Goals from Andros Townsend and Patrick van Aanholt had given Palace a 2-0 lead at Selhurst Park, but they failed to take anything out of the clash.
Chris Smalling and Romelu Lukaku struck before Nemanja Matic scored a 30-yard winner in the 91st minute.
Hodgson, whose team are a point adrift of safety, leaving the former England boss in a state of "total sadness" after his side were unable to take at least a point.
"Sadness. Total sadness," he said of his emotions post-game.
"I saw a group of players give their all for the club, for their team-mates against – on paper at least – overwhelming odds and to come away with nothing from the game, as we did on Sunday against Tottenham Hotspur, for the second time in a row… I feel very sad for them.
"I'm proud of the performance and I can't criticise any player for the effort or the work they put in, their discipline tactically. It's just one of those things, Lukaku scores a great equaliser and then in the very last minutes of the game the ball falls kindly and Matic scores a worldie from 25-30 metres which leaves the goalkeeper with no chance.
"If that ball goes over the crossbar or hits the crossbar and comes out or goes wide of the goal, I'd have been sitting here saying 'well done guys' and what a good performance, what a good point. As it is, you lose, so everything gets changed as a result."
RH: "I saw a group of players give their all for the club and their team mates. To come away with nothing like we did against Spurs for the second time in a row...I can't criticise any player. It's just one of those things." pic.twitter.com/cUl7vwjIoj— Crystal Palace F.C. (@CPFC) March 5, 2018
Palace are winless in six games, including losing their past three in the Premier League.
Hodgson still believes in his side's chances of remaining in the top flight.
"We're in the relegation zone, but after seven games everyone told me that we were relegated. At the moment we aren't relegated, we're in the relegation zone, so I think that's a positive," he said.
"We were eight points adrift of any sort of safety, now I think we're one point adrift of safety and there's lots of games to go.
"I don't think I should need convincing that the team has qualities. The team has determination and enormous fighting spirit."