In the opening 34 minutes, Palace scored three goals in a scintillating attacking display but twice conceded their two-goal lead.
“I thought our first half performance was very commanding but I was disappointed we conceded those two goals,” Hodgson said.
“In the second half Brighton put us under more pressure and we weren’t able to reproduce our level in terms of our attacking play so it meant we had to spend the last 15 minutes fighting to keep balls out of our box.
“We did it the easy way in the first half but the hard way in the second.”
The excellent Wilfried Zaha opened the scoring in the fifth minute by tapping in on the goal line after Mat Ryan had saved Luka Milivojevic’s shot.
A rampant Palace scored a second nine minutes later when James Tomkins scrambled the ball home at a corner but Glenn Murray halved Brighton’s deficit, hooking the ball in via the crossbar after Lewis Dunk had headed towards goal at another corner.
Zaha capitalised on more poor Brighton defending to head in his second from Milivojevic’s lofted cross in the 24th minute, only for the visitors to again pull a goal back 10 minutes later when Jose Izquierdo calmly finished across Wayne Hennessey.
Palace tired in the second half and rode their luck when Glenn Murray missed a straight-forward chance in stoppage time by failing to volley in Solly March’s cross from three yards.
However Hodsgon’s side held on for the win which moves them up to 16th in the table while Brighton are 13th with one point more than Palace and, with a difficult run-in to come, are still at risk of relegation.