Mohamed Salah (Getty Images)
Egyptian Football Association chairman Hany Abo Rida says the match officials "did not achieve justice" in the game.
The African giants loss 3-1 to Russia, combined with Saudi Arabia's defeat to Uruguay, ended both nations chances of progressing beyond the group stage.
Abo Rida, speaking from the Egyptian squad's World Cup base in Grozny, Chechnya, did not specify which incident would form the basis of the complaint.
The Egyptians contend that defender Ahmed Fathi was pushed before the ball deflected off him for an own goal that gave the Russians an early 1-0 lead.
The players also thought forward Mohsen Marwan should have been awarded a penalty when he was brought down inside the box. Both incidents took place in the second-half.
Egypt and Saudi Arabia meet Monday in Volgograd in their last Group A match.