Hurzeler is adamant they had their chances to take control of the game.
He said: "We controlled the game and played a good first half. Then into the second half we made too many easy mistakes and it was 3-1 out of nowhere and then we conceded the red card.
"The bad start to the second half has cost us. The red card didn't help; Joao (Pedro) has said sorry to the team and will learn from this.
"We then showed a great reaction and were close to making it 3-3 but in the end it wasn't good enough.
"At 3-1 I tried to put some fast players on the pitch with Kaoru Mitoma and Solly March and more midfielders so we could have more control of the game. In the end we didn't get the credit for the courage we showed but I was happy with our reaction. That was the plus from today.
"It's not about confidence because the reaction to the first goal and then when it was 3-1 was good. Of course it's easier when you are winning but in these moments you have to show personality and character.
"There are always tough moments in the season - we need everyone to stick together and show we are a big unit. I like the pressure, I will have to be the role model and we will find a solution (to finish the season strongly). I have to analyse it and then we have to find solutions."
"We need to play more as a team"
Meanwhile, Danny Welbeck - who scored on the day - admits Brighton fell short of standards.
He said: “We put our foot in it – we didn’t start the second half good enough and in the Premier League you can’t do that – you will get punished. They got a bit of momentum and put us in a really difficult position for the end of the game.
“We know as a team we can do better.
"We need to play much more collectively as a team, there have been too many of these performances throughout the season. We had some good spells, but we need to improve massively and fight for each other more as a team. We have made our bed and we have to lie in it."
Welbeck also offered an update on Jan-Paul van Hecke, who suffered a head injury in a collision.
“JP is conscious but he’s a bit groggy. He’s a warrior and hopefully he’s okay and can make a quick recovery. Hopefully it’s nothing too serious and he can fight through this.”