Real winger Lucas Vazquez was sent off for Real while Brazil wonderkid Vinicius Junior was controversially denied a penalty - as the European champions dropped further in the title race.
After the 2-2 draw with Villarreal for their opening fixture of 2019, the 2-1 loss to Sociedad has added woes of the Spanish giants and their manager Santiago Solari.
"The referee played a big role in things," he said. "I've always defended the VAR system, but it has to be improved because what we've seen was scandalous.
"He could have awarded the penalty and then consulted the VAR. After seeing the penalty incidents in the dressing room, all we ask for is fairness.
"There are times when we're punished for our behaviour on the pitch and the referees' committee should do the same with the officials. The VAR is in place but you've got to know how to use it and consult it.
"We're motivated and fighting for a La Liga title that'll be tough and it's made all the more difficult when things like this happen.
"When you're out there on the pitch it's so much more difficult because your heart is racing. As the team captain, I always try and help the referees, but tonight's performance was scandalous.
"Lucas Vazquez's sending-off was very harsh. Never before have I seen a player shown a second yellow for something like that, where you're in the middle of the pitch with three Real Madrid players around you."
Real sit a lowly fifth in La Liga, a point off fourth-placed Alaves and a huge 10 points adrift of Clasico rivals and league leaders Barcelona.