Palace were beaten 2-0 by United at Selhurst Park but were left frustrated after Wilfred Zaha had a penalty claim turned down with the scores level and Hodgson feels his side have a right to rue the decision.
Speaking after the game, the 72-year-old coach said: "We're not fortunate at the moment. The gods of fortune aren't smiling on us.
"Firstly with certain decisions, but they're not smiling on us as we're doing so well in so many areas and we're not getting rewards for the efforts. My feelings go out to the players as they couldn't have done more. We've won games against top teams like Manchester United playing a lot worse than we did tonight."
United manager Ole Gunnar Solskjaer felt that the officials had got the call right while Hodgson sees little point in reflecting on the incident.
The former England boss said: "You're always going to believe that when decisions go against you like that, they're wrong but I'm sure Ole has said the decision is right.
"I find that toing and froing pretty meaningless. It wasn't a penalty as the referee didn't give it and the VAR didn't overturn it. And we feel hard done by again but there are no points for feeling hard done by."