Carlo Ancelotti's side are now without a win in three games in all competitions but remain top of the table on 17 points, ahead of city rivals Atletico Madrid, who beat Barcelona 2-0 on Saturday, on goal difference
Real Madrid's stuttering form continued on Sunday when they were stunned 2-1 away at Espanyol in LaLiga.
Carlo Ancelotti's side are now without a win in three games in all competitions but remain top of the table on 17 points, ahead of city rivals Atletico Madrid, who beat Barcelona 2-0 on Saturday, on goal difference.
A goal in either half from Raul De Tomas and Aleix Vidal was enough for Espanyol to secure the three points against Real. The Catalans moved up to 12th with nine points.
"We weren't comfy. We conceded early and that makes the game tougher for you," Real defender Nacho said.
"They got in behind us a lot, and we need to work on our defensive play and that will come with games.
"We've got a number of players missing but we still have a good squad and we should be doing better than in our last three games. We need to improve at the back and respond."
Former Real Madrid youth team player De Tomas opened the scoring on 17 minutes after Ardi Embarba got in behind David Alaba down the visitors' left and squared across goal.
Eder Militao headed wide on the stroke of halftime as Real sought a way back into the game but they found themselves two down when Vidal danced his way through the middle of the park on the hour.
Sergi Darder missed a glorious chance to make it three before Karim Benzema's curled effort halved the deficit 19 minutes from time. Real, though, were unable to find an equaliser, with Eden Hazard's late effort ruled out for offside.