Pascal Gross had Brighton ahead on 70 minutes before Beto leveled seven minutes into injury-time.
“It was painful end to the game,” admitted Hurzeler afterwards.
“We started the game well and I thought we controlled the first half. At the start of the second half Everton caused us more problems.
“But our subs made a good impact and we scored a good goal. It was a good finish by Pascal and I’m pleased for him and Babis (Kostoulas) did well in the build-up with the dummy.
“Their goal at the end is something that happens in football.
“It’s tough but there are two options. You can feel self-pity or you can take ownership and responsibility and show a great reaction. That (second option) is our choice and there is another opportunity next week to do that.”
“But we know we have to manage the key moments in the game better and one bad moment has cost us the game.”