The left-handed Indian lost 6-7(4) 6-7 (1) to Joyce, who represents Ohio state in the US Collegiate circuit and is yet to turn a Pro.
Prajnesh, ranked 244, could convert none of the five break chances he earned but saved all four breakpoint he faced in the first round, which lasted one hour 34 minutes.
"I played well but did not do enough with the second serve returns. The match was decided mostly with that. I could have played better in tie-breakers but he took his chances in the tie-breaker," Prajnesh told PTI from Columbus.
Talking about his opponent, Prajnesh said,"he will be good when he comes out of college, if he chooses to do."
India have top players Yuki Bhambri and Ramkumar Ramanathan in the singles draw.
Yuki, seeded third and world number 156, is up against Jose Hernandez-Fernandez, ranked 343.
Second seed Ramkumar, ranked 153, will open his campaign against American Sekou Bangoura, ranked 379.
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