Christian Benteke scored a dramatic 95th-minute winner at the Amex Stadium after Brighton had dominated the match.
After calls from an influential group of Palace fans last week for the club to move on from Hodgson's "spineless, defensive tactics", the Eagles had only two touches in the Brighton box, two shots on target compared to 25 from their opponents and just 25 per cent possession.
Brighton defender Joel Veltman said Palace had pulled off a "robbery of the points", but a defiant Hodgson said: "The game's not about touches in the opposition box, is it? The game's about scoring goals and not letting any in.
"The statistic that counts at the end of the day is goals against and goals for.
"Okay, they had the better of possession, that's for sure, they had the ball in our box more often, they had more quality but I'm not going to apologise for coming away with what we consider to be a very good victory."