The Indian qualifier, ranked 110, pushed his opponent before bowing out with a 7-6(4) 4-6 4-6 loss, which came after an intense battle lasting two hours and 20 minutes.
The 25-year-old Indian saved 11 of the 15 breakpoints in the gruelling match.
The 45 points he earned by making the third round and 16 from the qualifying event, are likely to push Bhambri back to top-100 when the new rankings are issued on Monday.
Bhambri said playing Frenchman Pouille and Querrey was very different.
"They were completely different opponent. Sam has bigger serve and relies a lot on it. That was the difference today. He bailed himself out on a lot of points. Losing serve early in the third set was tough as I was playing catching up after that and more difficult against a big server," Bhambri told PTI.
The Indian Davis Cupper, who also beat world number 22 Gael Monfils in August 2017, said he has got a lot of confidence from the tournament.
"I feel, I can beat anyone. I just ned to keep giving myself the opportunities to do that," he said.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)