Karl Toko Ekambi delivered the decisive strike in the 124th minute in Blida on Wednesday (AEDT) to condemn Algeria to a 2-1 aggregate loss on away goals, with Cameroon qualifying for Qatar 2022.
Islam Slimani saw two goals ruled out, the first in the second half and again in extra time, with referee Bakary Gassama initially allowing the latter finish to stand before using the pitch-side monitor to deem the Algeria striker had handled the ball.
Charaf-Eddine Amara has resigned as president of FAF left in the wake of Algeria's exit from World Cup qualifying, while the federation has lodged an appeal to world governing body FIFA.
"The Algerian Football Federation (FAF) has lodged an appeal with the International Federation of Association Football (FIFA) against the scandalous arbitration which distorted the result of the Algeria-Cameroon play-off," the statement read.
"The FAF is determined to use all legally permitted means to have its rights restored and to replay the match under conditions guaranteeing the honesty and partiality of the arbitration.
"The FAF also requests the opening of an investigation by FIFA bodies to shed light on the arbitration of the Algeria-Cameroon match."
The draw for the group stage of the World Cup is set to take place on Saturday (AEDT).