The Seagulls go to St Mary's on Saturday on the back of an impressive 3-0 win against Chelsea.
Hurzeler said this morning: "It's about our performance, it's about improving ourselves. Tomorrow we have the chance to push our limits and show that we are going the right way.
"In the end, we play at Southampton, but we play at our own standards, pushing our own limits. There is no difference in our approach, no matter the opponent."
The Seagulls sit in tenth place on the Premier League table, seven points from the top four.
Asked about European qualification, Hurzeler continued: "We have clear goals and a clear vision but of course, it's an internal thing and as I always say we take it game by game.
"It's important now to keep the momentum, we've worked hard for it as nothing flies to us, we have to invest to get the results."
Asked for an update on James Milner, Hurzeler insists the veteran can play again this season.
The midfielder is recovering from a thigh injury and Hurzeler said: "If someone can do it, it's James. He's a special character, who has a special work ethic and mindset, so we will see whether we we will him back on the pitch.
"At the moment, he's doing very well in rehab and training very well. He's also very supportive not just for the players who are playing but also for me and the coaching staff. We are very happy he's around us but the most important thing is getting him back on the pitch."