Klopp watched on as former Dortmund man Robert Lewandowski marked his first league return to Signal Iduna Park with the only goal in a tight contest.
Lewandowski nodded in a rebound after Thomas Muller's shot was saved by Roman Weidenfeller and, despite enjoying the majority of possession after the interval, Dortmund failed to force an equaliser.
Defeat capped a miserable day for Dortmund, after their team bus was attacked prior to the game.
None of the players were in the bus at the time, as the vehicle suffered a smashed window and a damaged rear wheel while parked outside the team's hotel.
"The first 10 minutes were completely fine," Klopp said. "After that it was not so good, we had too few chances.
"Bayern sat deep and played very physically robust, we could not get our way. In the last zone we lacked punch.
"The second half was okay because we had our opportunities but, overall, it was not enough against Bayern. We lacked clarity.
"In many small moments Bayern were better, so they deserved to win."
Mats Hummels rued Marco Reus' miss on the hour, when the forward fired wide with just Manuel Neuer to beat, while the goalkeeper also produced a superb save two minutes from time to keep out the Germany attacker's free-kick.
"The effectiveness has made all the difference," Hummels said. "Bayern were not the better team, I can only remember two chances. We had not much more, but a bit more.
"It is unfortunate to have lost. Unfortunately you do not get 15 chances against Bayern.
"We had a huge opportunity when Marco ran alone on Neuer. And the free-kick at the end, he [Neuer] showed he's world class."
