The RBS-sponsored British number one tumbled out of the Pacific Life Open after a 2-6, 7-5, 6-3 defeat by the German.
After reaching the semis of the event last year, the result saw Murray drop two places in the world rankings to 13th.
"I didn't serve well enough and I was a bit too defensive on the break points in the third set," said Murray. "But to be fair to (Tommy), he did serve very well on a lot of (the break points) and didn't give me any cheap points. So credit to him for that."
Murray added: "I don't think that I missed any sitters, I didn't make any mistakes. But I guess if I was playing a bit more aggressive – a lot like I was in the first set – coming to the net and taking my chances a bit better, I think I would have won the match."
Murray advanced to the last 16 with wins over Jurgen Melzer and Ivo Karlovic, both in three sets. And when he cruised through the opening set against Haas it looked as if he was on track for a repeat of his Dubai showdown with world number one Roger Federer.
However, the German (who retired with a sinus infection without striking a ball in the quarter-finals) fought back. He took a second set that could have gone either way before taking control in the decider.
"I'll learn from it because stuff I did out there in the first set showed me I can play very good tennis and win a set really comfortably against someone as good as him," added Murray. "It's a consistency thing and making sure you do it the whole way through the match."
The title was eventually won by Novak Djokovic, who defeated the unseeded American, Mardy Fish, 6-2, 5-7, 6-3.
Meanwhile, Andy's brother, Jamie, who is also sponsored by RBS, progressed to the semi-finals of the men's doubles at the Pacific Life Open with playing partner Max Mirnyi.
The duo defeated top-seeded Americans Bob and Mike Bryan after a match tie-break, 5-7 6-4 (10-6), but lost in the last four to Jonathan Erlich and Andy Ram.