Faced with a side who had lost their last eight competitive fixtures, Klopp believes his players took the task too lightly, and were punished as a result.
"There's an old saying that a good horse only jumps as high as he has to," Klopp said.
"Well I hate this saying more than anything. I think a horse should jump as high as it can.
"We looked at how high we had to jump today and, when we realised that it wasn't so high, we had already fallen behind."
Hamburg coach Mirko Slomka had another explanation for his side's victory.
"Taming this Dortmund side takes a lot of passion, will to run, will to fight and the will to keep chasing the ball," he told Sky television.
"We did so much of the things we had set out to do. We played like a team and that is what we need.
"There are certainly still many things we can do better and which we've got to work on over the coming weeks."
It was nevertheless a step in the right direction for Hamburg, who moved out of the bottom two thanks also to a wonder goal from Hakan Calhanoglu, who lobbed Roman Weidenfeller with a free-kick from near the halfway line.
"It was magnificent," Slomka said. "But Hakan can do that; he practises it in training.
"It's good when he gives it a go. I thought it was pretty courageous of him because I thought it was best to keep the ball and run the clock down, but scoring a goal's even better, of course."