Sociedad took the lead through Willian Jose's penalty just three minutes into the match and had Lucas Vasquez sent off before Ruben Pardo wrapped it up late on for the hosts.

But while the game was at 1-0, Vinicius Junior tumbled under a challenge from Sociedad goalkeeper Geronimo Rulli and replays suggested it was a clear foul.

New @RealSociedadEN manager Imanol Alguacil wins at the Bernabeu in his first match in charge! 💪💙#RealMadridRealSociedad 0-2 pic.twitter.com/THY1Idfyu9

— LaLiga (@LaLigaEN) January 6, 2019

However, VAR did not intervene and Madrid did not get their spot-kick.

"We have not talked to the referee," coach Santiago Solari said. "There are plays that seem obvious when you watch them live and others that are not, and we believe VAR is for that – when there is no certainty we can consult it.

"If it is not for this then it loses all reason to be. We are all human and we all make mistakes but if we have the option to review the evidence and you do not, it is difficult to understand."

Vinicius was making his full league debut and was the sole bright point for Madrid in a disappointing afternoon.

Vinicius Junior felt he should have a had a penalty on his full Real Madrid debut (Paul White/AP/PA)

"Players grow with time and maturity," Solari said of the Brazilian. "He is 18-years-old and has been a joy since he came to the club aged 17. He has already scored a goal in the Club World Cup final and his progress has been much faster than expected."

Defeat left Madrid with their joint-worst points tally at this stage of a season in the 21st century, but Solari insisted he was happy with the fighting spirit shown by his side – even if large portions of home crowd seemed to disagree as boos rained down.

"We compete to win, we always fight to win," he said. "We never underestimate the competition or anything or anyone. That is the winning character and we have shown that character. I saw it today. Not seeing that would be unforgivable."

What it means to get your first win at the Bernabeu in 15 years! 🤩#RealMadridRealSociedad pic.twitter.com/iLloyaXFoj

— LaLiga (@LaLigaEN) January 6, 2019

The victory was the first for Sociedad coach Imanol Alguacil since he returned to the position on December 26.

"To win here you have to face everything and be lucky," he said "The players have done a special job.

"Playing with such personality is not easy. I am proud of my players because to win here you have to do a lot.

Good win to start 2019 ! 💥💫🙏🏻 pic.twitter.com/Lfp9VDDnaR

— Adnan Januzaj (@adnanjanuzaj) January 6, 2019

Asked about the penalty call involving Vinicius, Imanol backed his goalkeeper but admitted he could not be sure.

"I'll be honest, I think the trajectory of the ball indicates that he plays it, but I have not talked to the players," Algucil added.

"It's true there have been a couple of doubtful plays but from the bench I can't say."

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