The champions have demanded a "structural reform" of refereeing in Spain amid a withering assessment of the performances of match official Alejandro Muniz Ruiz and VAR Javier Iglesias Villanueva.
Real's grievances centre on Espanyol's Carlos Romero, who went on the score the game's only goal, after only being booked for what the club felt was a "brutal" challenge on Kylian Mbappe.
They were also unhappy that Vinicius Junior had a goal ruled out.
The letter, which is addressed to RFEF president Rafael Louzan, read: "The events that occurred in this match have exceeded any margin of human error or referee interpretation.
"What happened at the RCDE Stadium represents the culmination of a completely discredited refereeing system, in which the decisions against Real Madrid have reached a level of manipulation and adulteration of the competition that can no longer be ignored."
In a lengthy letter, Real Madrid claim Romero's tackle on Mbappe was "deserving of immediate expulsion" and the decision not to send him off, which was confirmed by VAR, was "manifestly erroneous". Head coach Carlo Ancelotti described it as "inexplicable".
They also say the incident in which the Vinicius 'goal' was chalked off for a foul by Mbappe earlier in the move, should in fact have resulted in a penalty to them.
The letter continues: "The scandal generated by this match has once again had worldwide repercussions, with the international press denouncing the biased use of the VAR in Spain and the lack of credibility of Spanish refereeing."
Madrid currently top La Liga by a point from city rivals Atletico, with Barcelona four points behind.
On Monday night, Girona beat Las Palmas 2-1 to end a four-game losing streak.
The hosts drew first blood after seven minutes when Abel Ruiz beat the offside trap and coolly slotted the ball under the advancing goalkeeper.
The burly striker missed a chance to double the lead when his penalty was saved on the stroke of halftime, but Colombian winger Yaser Asprilla made it 2-0 after 79 minutes with a fine low shot from the edge of the box.
Fabio Silva scored a consolation goal three minutes later for the visitors.
Girona go seventh in the standings while Las Palmas are two points above the relegation zone.
With AP.
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