Dortmund lost for the seventh in the Bundesliga this season as rivals Bayern Munich retained a 20-point advantage at the summit.
Goals from Raffael and Max Kruse gave Monchengladbach a two-goal advantage at half-time, with Milos Jojic reducing the deficit late on.
Klopp thought that his side had levelled when substitute Marvin Ducksch fired home, but Robert Lewandowski had been penalised for a foul in the build-up.
That decision left Klopp irate and he was sent to the stands for his protestations, compounding a miserable day for the Dortmund coach.
"I have rarely seen a first half like this one," he said. "We didn't do much wrong and shouldn't really have been 2-0 behind.
"We just lost three crucial duels that led to the two goals like Patrick Herrmann's chance when we let him go through at the second post, we should have been stronger.
"Nevertheless we had the feeling in the second half that we could sort things out.
"We leave empty handed but there were a lot of positive aspects today.
"I will always tell the team in private when I think they didn't do enough but today, that wasn't the case."
