Adrian Ramos has missed three glaring chances before Dortmund allowed Jairo to get a cross in and left Shinji Okazaki unmarked to break the deadlock at the Coface Arena.
Then, after Ciro Immobile had missed the chance to equalise from the penalty spot, more disorganised defending then leg to Matthias Ginter putting through his own net to put the game out of Dortmund's reach.
"We could have been worthy winners if we had taken our chances," said Klopp. "Instead, we defended poorly twice and were deserved losers.
"We had a lot of good moments in the game. We started very well but then took our feet off the gas.
"But if you concede two goals in the second half, you deserve to lose. We should have been much more active for their first goal. We defended badly today.
"Adrian [Ramos] also could have taken one of his chances. Today he didn't manage to. In a game like this you need those things to go for you.
"And Ciro didn't make a clean connection on his penalty. It happens in football."
Erik Durm, who began his career at Mainz as a striker before Jurgen Klopp converted him into a full-back, also rued Dortmund's wasteful finishing.
"We played well for the first 20, 30 minutes. We got forward and created good opportunities.
"However, we must be more clinical in front of goal."