The hosts claimed victory over their fierce rivals thanks to quickfire strikes from Joel Matip and Eric Maxim Choupo-Moting on Saturday, as Dortmund failed to arrest their disappointing start to the campaign.
Last year's runners-up have now lost three of their opening six Bundesliga fixtures, with Klopp accepting that failings at the back have played a major part.
"Rarely do you win games in football conceding goals like that," the 47-year-old told reporters.
"We conceded two goals that have nothing to do with tactics.
"You have to be ready and we were not in at least two situations today."
Dortmund were missing several key players for the short trip to Gelsenkirchen, including Nuri Sahin, Henrikh Mkhitaryan and Marco Reus, although World Cup-winning defender Mats Hummels did make his first start of the campaign.
But Hummels' return proved to be a turbulent one, with the visitors finding themselves two goals behind after just 23 minutes.
And although the in-form Pierre-Emerick Aubameyang managed to reduce the deficit before the break, Klopp's men were unable to rescue a point.
"In the second half we pressed but the clear chances have been lacking," added Klopp, who also issued a rallying-cry for his players.
"This is of course anything but a good start for us," he continued.
"We have several problems with which we deal differently, but believe me [on] one thing: we will come good!"
