Dortmund’s fifth straight Bundesliga defeat has seen last season’s runners-up tumble to third from bottom in the table and their worst-ever start to a campaign is piling the pressure on Klopp who led them to league titles in 2011 and 2012.
Describing his team’s position as “just horrible”, he told reporters at the Allianz Arena: “We still have a lot of construction sites in our squad.
“One could see that today. It is not just through bad luck that we are languishing down there.
“We played our best first half in a long time. We have to start being rewarded for our effort. That is bothering us.”
Dortmund gave Bayern a run for their money in the opening period, pressing high and launching breaks in their trademark lightning-quick style including one which gave them the lead through Marco Reus.
They then lost captain Mats Hummels through injury at halftime, depriving them of some defensive consistency, while the visitors also failed to maintain the same level of pressure at the other end of the pitch.
Two mistakes by substitute defender Neven Subotic were enough to turn the game in Bayern’s favour in the second half as goals from Robert Lewandowski and Arjen Robben, with an 85th-minute penalty, secured a comeback win.
“Fact is we played very little football in the second half. We became too passive,” said Klopp whose team host Galatasaray in the Champions League next week after having won all three games so far to lead Group D.
“We should not change our play like we did in the second half.”
Dortmund have picked up just seven points from their first 10 league games.
(Reporting by Karolos Grohmann; Edited by Ian Chadband)