Mats Wieffer struck both goals for the visitors at Turf Moor.
Hurzeler said afterwards: "First of all, I want to say thankful for our supporters for travelling so far and I hope the result means they have a good journey back. Regarding the performance, I think it was not the best game from us. We got the clean sheet - that was important - but we suffered, especially at the defensive set pieces. In two moments we were a little bit lucky because we (had) offside positions.
"The Premier League is so competitive, there is no easy game. The approach from us, the effort was good. It was not an easy game, not a perfect performance, but it's important to win these kind of games."
Hurzeler was keen to highlight the unity amongst the players.
"Players who are not playing should be frustrated because everyone should have the expectation to play. But (the players) wait for their chance; they are very patient. Every player during the season will be important for us. That’s team togetherness," he added.
"I’m not a biggest fan of talking about Europe - that’s more from the media side. Overall, we are known for our expectations, for being ambitious. We want to achieve something; we want to make the next step as a team.
"But the most important thing is that we need to understand that we need to earn the right to compete with the top teams. Earning the right means staying humble, working hard every day and bringing consistency into the performances. If you get the consistency right, we proved we can compete with the big teams."