Marcus Tavernier had Bournemouth ahead midway through the first-half via a penalty before Charalampos Kostoulas struck a superb overhead goal a minute into injury time for Brighton's equaliser.
Hurzeler said afterwards: "In the end we lost the rhythm after we conceded the goal, and that is something we have to do better. In the second half we had big opportunities. We wanted to win this game, in the end we have to accept the point, but I think we definitely deserved to win this game.
"We wasted 20 minutes in the first half after the goal and we could use them much more effectively. In the second half we were better in positioning and then I think that we had the game under control and we could score more than one goal."
On the Bournemouth penalty, the manager said: "A lot of people have different views on that. In the end I think that if you really see it, I don't see a penalty there. I don't know why (his assistant was booked), he was only watching from our bench. It was an emotional game. You will have to ask the referee."
On Kostoulas' equaliser, Hurzeler continued: "Yes nice goal. We all know what he is capable of. But, we all prefer to win.
"We need to make the small margins right and that is what we definitely have to improve. We keep on working and we need to understand that we need to bring a consistency into our behaviours. That is what we will work on."