Chelsea had the lead through through an own goal from Brighton goalkeeper Bart Verbruggen. However, the Seagulls fought back to win 2-1 thanks to efforts from Georginio Rutter and Kaoru Mitoma. Chelsea felt Mitoma's winner should've been disallowed for a handball incident in the lead-up.
Hurzeler said afterwards: "Great reaction. We showed character after that start. I'm proud of how they came back. It's not easy. That's why it was well deserved.
"Mistakes happen. If a keeper makes a mistake normally it's a goal. We try to support him because he's a great goalkeeper.
"Georginio Rutter is doing good. He adapted quickly to the intensity of the Premier League. He has great skills and showed it today.
"It was a togetherness on the pitch. It's a team performance. They bounced back, they stuck together. They didn't point fingers after losing. They took ownership."
On no VAR, he added: "But that's it. That's football. With VAR football is getting not that emotional like today. Everyone agrees that today was a great atmosphere. They can celebrate a goal because they know it's a goal. I'm happy it was like that.
"We always try to stay grounded and work hard. We try not to get euphoric after a good win or panic after a defeat.
"That's why we all love football because you can bounce back. It's not always going up, it's downs. In life it's important to know a successful journey is not a comfortable journey."