Leading through Yasin Ayari until 71 minutes, Brighton fell to goals from Samu Chukwueze and Harry Wilson on 92 minutes for Fulham.
Hurzeler said, "Sometimes the better team loses and we have to accept it. But it was one of our best performances so far.
"I think we were quite strong today. We created a lot of chances and were the better team. But sometimes football is brutal. We were pleased with the performance, but not the result."
"We can't control individual errors or VAR," he added. "We have to accept errors happen sometimes and try to do better. Bart has had a great season and sometimes these things happen.
"If there weren't errors there would never be any goals but I would never put any responsibility on Bart (Verbruggen) or Ollie (Boscagli). We defended well and controlled the game."