Willian Jose got La Real off to a great start, scoring a penalty in the third minute after Casemiro clumsily felled Mikel Merino in the box.
After the break, Lucas Vazquez was dismissed for a second booking and then Vinicius seemed to be denied a clear penalty, the Brazilian going to ground after seeming to beat the sprawling Geronimo Rulli to the ball.
No spot-kick was awarded and Ruben Pardo sealed the points late on, and Solari – who is under increasing pressure – is convinced his team were hard done by.
"Everything went against us," Solari told Movistar.
"We did not get into the game well, we had an unfortunate move in the second minute.
"We did everything to turn it around and did not get any goal. We have had chances, but did not put them in.
"And then there was that play that nobody understood why it didn't end with a penalty. It seems to me like a textbook penalty."
In his post-match news conference, the Argentinian was eager to show some understanding towards the officials, though he was confused as to why no review of the incident appeared to happen.
"We have not spoken with the referees," he told reporters.
"There are plays that seem obvious in real time, but we believe VAR technology is there to check.
"We are all humans and make mistakes, but if you do not check to correct the mistake, it is difficult to understand."