The unseeded Indian had the advantage after winning the first set but the 17th seed Souza shut the door on him with a 4-6, 6-2, 8-6 triumph in the opening round of the clay court Major's qualifying event.
Amritraj's first and only appearance in a Grand Slam main draw was way back in 2002 when he entered the US Open as a wild card.
Now Indian hopes rest on Somdev Devvarman, who has advanced to the second round after he beat Jiri Vanek on Monday.
Somdev will next take on Kiwi Daniel King-Turner.