VAR ruled that Maxi Gomez was onside when collecting a pass from Rodrigo Moreno in the build-up to Cheryshev's 27th-minute strike, which proved to be the winning goal at San Mames.
Confusion arose when lines added to the live television footage of Cheryshev's goal initially showed he was marginally offside, though the VAR officials had a different view of the incident and adjudged the goal should stand.
The official VAR line used by the officials did not appear on the TV footage until the second half of the match, doing little to clear up the uncertainty.
The RFEF has released a statement concerning the controversy.
"Against the most elementary rules of the ethical sporting code and the rules of national and international competition, the producer of the match has put up images of a hypothetical offside line that doesn't correspond to the [line] of VAR," the statement read.
"These images [are] without any sort of technical rigour and offer a distorted view of the play. [It's a] manoeuvre which creates a social alarm like a loss in confidence in the current VAR provider and in the skill of the Spanish referees.
"The RFEF wants to make it clear that there can be no confusion and will raise the relevant complaint to international judicial and football organisations to analyse the situation and apply the corresponding measures.
"We are convinced that these irresponsible actions could lead to serious penalties. Therefore, we urge the LNFP [the Spanish football league] to articulate the necessary mechanisms to cease these types of activities so as not to damage and devalue the image of Spanish football."