The Seagulls' winless run extended to a fourth game as Palace took home the spoils in the M23 derby with a 3-1 victory on Sunday.
A first-half strike from Trevoh Calobah and Ismaila Sarr's double put the visitors up 3-0, although an own goal from Marc Guehi gave Brighton a late consolation.
However, Hurzeler was left fuming over the build-up that led to Chalobah's opener.
As Crystal Palace mounted a counter-attack, referee Oliver accidentally got in the way of Carlos Baleba.
The counter-attack ended with Palace winning a corner, from which another corner followed.
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It was from the second corner Chalobah slammed the ball into the roof of the net to give Palace the lead.
But speaking after the match, Hurzeler revealed it should never have got to that point thanks to Oliver's error.
"When the referee says after the game it is his mistake, I don't understand why he doesn't stop the game," Hurzeler said.
"Unbelievable for something like this to happen."
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Although Hurzeler could have complaints about the lead-up to Chalobah's goal, there was little he could moan about regarding Sarr's double.
Seagulls right-back Tariq Lamptey completely misjudged a high ball that allowed Palace's Tyrick Mitchell to control the ball and whip in an inviting cross that Sarr headed home.
Lewis Dunk became the next Brighton defender to serve up a costly error when he lost a physical challenge against Eddie Nketiah.
He allowed Sarr to brush the Seagulls skipper aside before coolly slotting past Bart Verbruggen for Palace's third.
Nketiah had a golden chance to open his Premier League account for Palace after Guehi's own goal as all of Brighton's defenders were inside the visitors' half.
However, the former Arsenal forward's chipped effort over the on-rushing Verbruggen landed wide of the goal.
Brighton had their chances throughout, but several superb stops from Eagles gloveman Dean Henderson kept them out.
Henderson's finest save came when he produced a fingertip effort with his left hand to turn Julio Enciso's driven strike past the left post.
The defeat to Palace marked the first time Hurzeler had tasted defeat at home as Brighton manager.
It was also the first time in six games Palace had recorded a win over Brighton in the league.
Another remarkable stat to emerge from the contest was the fact Brighton's loss marked their 60th defeat in their last 180 Premier League fixtures, with 60 wins and 60 draws rounding out the figure.
Hurzeler and his squad will look to avoid their winless streak extending to a fifth match when they travel to the capital next week.
They are now preparing for a crucial clash against West Ham United on December 21.