Germany looked on course for victory after Felix Nmecha scored before Cody Gakpo struck late to rescue a point for the Netherlands.
Klopp was pleased with the mentality shown by his players but admitted there was plenty of room for improvement.
"I was very, very, very pleased with a lot of the individual performances," Klopp told RTL. "Overall, I was very happy with the passion we showed. We can play better and play more football, that's for sure.
"We created work for ourselves, which meant we had to run and put in the effort - it was demanding for both teams. I would have really loved to win, but I'm happy enough with the point."
Klopp, who has spent more than 1,000 matches on the touchline during his coaching career, said the experience of leading Germany felt familiar despite the change of environment.
"I've stood on the touchline more than 1,000 times, so I know the position and that hasn't changed," he said.
The Germany coach also addressed Serge Gnabry's role in the Netherlands' equaliser.
Gnabry lost possession in the closing stages, allowing the Dutch to launch the attack that ended with Gakpo finding the net. Klopp felt the Bayern Munich forward should have made a different decision.
"That's not a problem, it can happen. But Serge has to run forward in that moment," Klopp said.
"He has to take his first touch forward with the ball when you still have 20 or 30 seconds to play. But Serge obviously knows that too."
Former Germany international Lothar Matthaus also pointed to the mistake, although he praised the quality of the Dutch attack.
"That was a great attack, but Gnabry must not lose the ball and he has to track back faster," Matthaus said.
Klopp will now turn his attention to Germany's next challenge, with Greece awaiting on Sunday.
