A late penalty from Luka Milivojevic proved to be only a mild tonic for the Eagles at Goodison Park after the Toffees confidently sealed up the contest thanks to second-half goals from Gylfi Sigurdsson, Oumar Niasse and Tom Davies.
After an impressive run that saw Palace move from zero points up to 14th in the table, Hodgson's side are now without a win in their last four and back to within two points of the dropzone.
"The first half we were good value, certainly for 0-0 and we were confident we could keep going but the early goal in the second half puts you on the back foot," Hodgson told BBC Sport at Goodison. "We played some reasonable football but it was difficult to get back after 2-0, the third goal killed us off. It was a sterling effort from the players and the way they went abut their business. We have to accept we were beaten.
"We made our mistakes for the goals and were punished for them. The rest of the time we put a reasonable shot. We gave ourselves a mountain to climb after gong 2-0 down.
"There is a certain frustration at the moment because we have not had things going our way, especially with injuries. We have so many out, including important ones. The 11 who started the game gave a good account of themselves.
"Defeats do eat into your confidence, just like wins boost your confidence. The players are aware what they are capable of and what they need to do. In these two weeks, I hope to recover a couple of players. Every game is a difficult one and we have to believe every game will be a scrap and a fight."
Next up for Palace is a tough home encounter with Tottenham Hotspur on February 26.