Referee Cesar Ramos booked Sofiane Boufal following a challenge by Theo Hernandez, which Morocco thought should have been a penalty
The FMRF is unhappy that Mexican referee Cesar Ramos failed to award a penalty in the first half to the North Africans when Theo Hernandez made contact with Sofiane Boufal in the area.
Instead of awarding a spot-kick, which several neutrals felt was appropriate, Ramos instead booked winger Boufal for a foul.
The Moroccans were also unhappy that the hauling down of substitute Selim Amallah as he awaited the delivery of a set-piece also failed to prompt another look from officials.
The first African and Arab team to contest a World Cup semi-final, Morocco lost 2-0 after an early goal by left-back Hernandez was followed by a late strike from substitute Randal Kolo Muani.
"The FMRF has written to the relevant body to review the refereeing decisions that deprived the Moroccan team of two penalties that were indisputable in the view of several refereeing specialists," the Moroccan ruling body said in a statement.
"The FMRF was equally astonished that the video assistant referee (VAR) did not react to these situations."
The lack of VAR intervention mystified some of those working as pundits during the game.
"It looked like a penalty to Morocco for me - VAR not working," asked former England striker Chris Sutton, who attended the game for domestic British radio.
It was an analysis with which former England defender Rio Ferdinand agreed.
"I thought it was a penalty on Sofiane Boufal, rather than a foul by him," the former Manchester United player, working as a television pundit, said.
BBC Sport Africa has contacted Fifa for comment regarding the Moroccan protest.
The Atlas Lions still have one game left in Qatar when they take on Croatia in Saturday's third-place play-off.
Having already defied expectations by overcoming Belgium, Spain and Portugal en route to the last four, the Atlas Lions can now become the first African team to ever take an effective bronze medal at the World Cup.
-- Courtesy of BBC Sport