The peasants lost to second-division side Canal Mooring & Lights 4-3 on penalties after a 2-2 draw to suffer a first-round exit from Egypt's oldest competition.
They could not retain their top flight status after a 1-1 draw at Harras Hodoud last Monday condemned them to relegation.
Canal Mooring & Lights, the second lower division side to book a last-16 berth after Ragaa, will face Petrojet in the second round.
Petrojet, who finished fourth in the Egyptian Premier League, crushed Qanah 3-0.
Military Production could have become the second Premier League team to be eliminated but struck in stoppage time to spare their blushes against Nassr.
Nassr took a surprise lead two minutes before the break but striker Hassan Mousa brought Production level on 70 minutes.
A late goal from Hassan Awad prevented Production from following in the footsteps of Police Union, who were knocked out of the cup on Friday after a defeat at the hands of Ragaa.
Asyut Petroleum needed four goals from Wael Farrag to claim a 5-3 victory over Alexandria-based club Koroum in a thrilling game.
Gouna, who survived relegation on the final day of the season, went through after defeating Dakhlia 4-3 on penalties.
The normal and extra time ended in a 2-2 draw as Gouna forward Gamal Hamza scored twice.
The former Zamalek man will join Egyptian champions Ahli in the close season.