Three first-half goals stunned Palace, before Wilfried Zaha won a penalty late on which was converted by Luka Milivojevic.
The opening goal came in highly controversial circumstances when James McArthur won the ball in a challenge before Jose Izquierdo fell to ground. Referee Kevin Friend awarded a penalty which Glenn Murray converted.
Shane Duffy was sent off for an altercation with Patrick van Aanholt, but Brighton doubled their lead when Leon Balogun fired in with his first touch, before Florin Andone put the game out of sight just before half-time after beating James Tomkins in a foot race to smash low past Wayne Hennessey.
It was clear that the award of the penalty shook the Eagles, and Hodgson admitted his team failed to cope with it.
“We had to adjust and we didn’t,” said the former Fulham, Liverpool and West Bromwich Albion boss.
“The second and third goals are just as disappointing and frustrating, to use two buzzwords.
“When you come here hoping to win the game and you lose 3-1 there are no good feelings or anything particularly positive that I can say.
In every football match you can point to episodes and things being different but the second goal is something that we have to take total responsibility for and the third even more so; it wasn’t even an attack, just a clearance.
“Football does those things and you never know what will happen. The pattern of the game is impossible to envisage – things happen and you have to deal with them. In regards to the penalty, there’s no point in allowing that to totally disturb the way you want to play, irrespective of whether you think it was correctly or incorrectly given.
“You maybe have to make certain in those situations that you don’t compound it by conceding two other goals which are definitely going to put the home team in the ascendancy.
In every game there are so-called injustices and decisions that can be contested, from penalties to throw-ins. It’s a fact of life and something you have to deal with.”
With a paucity of talented options on the bench, it took until the 58th minute for any substitutions to be made, with Hodgson admitting that he had little in the way of options to freshen things up.
“I am always tempted but there are other games coming up,” he said.
“If I thought I could make a change that would put us in an undoubted position to win the game 4-3 with the players that are on the bench then I would have done it, but everybody knows as well as I do that we don’t have that type of player.
“Suddenly we’re 3-0 down against a team albeit with 10 men, and you know they believe they can win the game as long as they defend sensibly in the second half.
“We expected them to do that and they did. We dominated possession and tried our best and had plenty of moves and attempts, but it only led to the one goal and as a result we lost the game.
“All we can do now is pick ourselves up and remember how well we are capable of playing. We go home knowing that tonight was not the performance we wanted to give, and it certainly wasn’t the result we wanted, but the result is the result.
“There is nothing I can say or do that can change that, and there’s no point than accepting the fact that we lost on the night and congratulate Brighton on their victory.
“We have to make certain that we are learning lessons that are there to be learnt and put this game behind us so that it doesn’t have any effect in the games to come.”
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