Hughton’s team gave away three goals in the opening 24 minutes as Palace piled pressure on the Brighton goal.
Two of the goals were conceded from corners, which has been a frustrating way to concede by The Seagulls this season. The other was a Wilfred Zaha header, however, all the goals were a result of poor defending from Brighton.
Speaking after the game, Hughton said: "I don't think you can (explain it). You work in the week on set plays.”
"We haven't conceded a goal from a corner since West Brom, so that's hugely disappointing.”
"We conceded two goals from corners and one from the type of run that Zaha makes. We've certainly lost out because of the first half performance."
After 18 minutes of the heated derby Glenn Murray added to his impressive tally for the season to mark his 14th goal, Jose Izquierdo who also scored after 34 minutes, his fifth of the season to keep Brighton within a chance.
The Seagulls had a better second half but failed to score
Brighton kept battling and were the better side in the second half but were unable to add to the scoresheet, with former Palace player Murray missing a chance late on in the game.
Hughton said: "Did I expect him to (score?) Yes, probably on most occasions he would have put that away, but he's usually there."
Hughton went on to say: "It's a difficult period for us at the moment but there is enough in our game that gives us confidence that we can get results."
Brighton remain in 13th place with seven points off the relegation zone, with a tough run in.