His team started the game brightly but the tables turned after they fell behind to an impressive Connor Roberts opener.
By and large, the Saints struggled to cope with the adrenaline and the enthusiasm of their opponents and Nathan Collins killed the game off with a header at the end of the first-half.
On the game
Hasenhuttl pointed to the fact that the game could have been different if Oriol Romeu had scored in the opening stages of the match.
"We had the first big chance of the game with a free header from Oriol (Romeu) from a set piece," he said. "If we score this, the game goes in a different direction.
"We concede a goal with the first chance from them and after this we don't win any duels up until half-time. We don't deserve to get something because we have been lacking in everything after the first 15 minutes. It's simply not good enough.
"In the second half, we tried to change the shape a little bit with more power in the centre and we had two good chances from Che and we didn't score there. Otherwise, maybe in the end it's getting tighter.
"They defended quite well and we did not have the quality with the ball, or the braveness to find the right decision in and around the box. In the end, it was too easy for them to defend us. We were not dangerous enough in their half."
On fighting back
The Saints boss was not impressed with his side's display in the opening half but he wanted the same eleven to find a response.
"I gave them another 10-15 minutes to try to change things. We showed them where the spaces are that we can use. At half time, I could change all eleven players if I wanted to – well maybe ten – Fraser (Forster) was different.
"When you start like this against Burnley in this stadium then it's tough to come back. We tried in the second half and we were a little bit better but we were far away from deserving something today."
On the press
Hasenhuttl admitted that Southampton's press was not as good as it should have been and he felt that this contributed to his team's struggles.
"Because you are not defending out of the red zone brave enough. Normally, we are closing from the front much better but we have been too late. We were always on the reverse gear and we were not good enough."