The German head coach's side dominated possession throughout but were unable to break down a stubborn and determined away defence.
And as Town pushed deep into stoppage time in search of an elusive winning goal, they succumbed to a counter-attack which saw substitute Jackson Irvine seal all three points for the visitors.
The result dents Town's hopes of automatic promotion after a second successive league defeat with the Town boss left disappointed at his side's inability to produce more in the final third.
"It's disappointing, not just because of the result but because of our performance, especially with the ball in the final third” said Town's boss.
“We were not good enough in the offensive situations to create better opportunities – we were not quick enough and did not accelerate the game enough.”
"We showed a lack of quality and we have made too many wrong decisions."
Nigel Clough's side came to the John Smith's Stadium with a clear gameplan to slow the tempo of the match and disrupt the typically free-flowing football of the home side.
But it could have been so much different if full-back Tommy Smith had scored from a third minute opportunity or was awarded a penalty mid-way through the first half for a push in the box.
"It was a clear penalty and a clear foul, but saying that sounds like an excuse and I don't want to look for excuses,” said Wagner.
“Against a difficult opponent who came to slow the game down an early goal would certainly have helped.
“At the end we gave them a few counter-attacks and they have scored.
“This result hurts but the players tried everything and we still have eight games to go and we must stay focused."
The loss to Burton Albion told a similar tale to dropped points against fellow league strugglers Wigan Athletic and Blackburn Rovers where Huddersfield Town failed to convert their authority and dominance over lesser sides into victories.
David Wagner's side have thrived all season on a 'Terrier Spirit' which has positioned them as underdogs against the majority of Championship opponents.
But the boss was quick to refute claims his side struggle when they are apparent favourites in such encounters.
“In terms of our fighting identity and performance we tried everything until the final whistle,” Wagner added.
“We had a good balance for long periods behind the ball – we didn't give the opponent anything in terms of counter-attacks.
“It doesn't matter whether you are a big dog or not, it only depends on making too many wrong decisions.
“We see a lot of games where one side sits back and the other has a lot of ball possession but then lose on a counter-attack – it happens.
"On the one side you need to be patient and then on the other you have to accelerate the game.
“They played their way and got a result – we have to learn how to handle these opponents better than we did today.
“For this we have to score early and be more clinical in front of goal.”