Pospisil, the seventh seed, saved match points in each of the last two sets before falling to the unseeded Dutchman.
"I wasn't very happy with the way I was playing,"said Pospisil. "He played well and went for his shots. I'm aware that I didn't and it's something I'll work on.
"I wasn't feeling that great today in general, even in the warmup. But that's the way it goes. You have to do the best you can with what you have."
Pospisil jumped out to a 3-0 lead in the first-set tiebreaker before dropping seven straight points. The 23-year-old Canadian faced a match ball in the last game of the second set before pulling even and taking the tiebreaker.
However, Haase overwhelmed Pospisil in the deciding set on the cramped secondary court of the Statdhalle, completing the win in two hours 19 minutes.
Pospisil, a native of Vernon, B.C., had nine aces and kept the pressure on Haase with 12 break points, but the Dutchman saved 10 of them. The Canadian had his serve broken four times.
Pospisil is looking to close out the season strong so that he can achieve his goal of earning a seed for the Australian Open in January. Pospisil is currently ranked 40th in the world.
"I've had a great season," said Pospisil, who reached the Rogers Cup semifinals last August in Montreal. "Myself and my coach have set a goal of trying to get a seeding for Melbourne.
"It's a tough ask and I have to beat some good players to get there."
Pospisil defeated Lleyton Hewitt — a former world No. 1 — in the first round.