Real are now third in LaLiga, 14 points behind leaders and rivals FC Barcelona, who have a game in hand. Atletico hosts Leganes on Wednesday and Barcelona visits Las Palmas on Thursday.
"I'm angry for my players, because they conceded a goal in the last minute. the opposition did not enjoy many chances", said the Frenchman.
"We performed better in the first half than we did in the second", Varan said after the match.
Meanwhile, youngsters Borja Mayoral, Achraf Hakimi, Jesus Vallejo and Marcos Llorente have supposedly been deemed as not being up to scratch. Benzema replaced Isco in the 69th minute.
No sooner had Madrid impressed on Saturday against Alaves by winning five fixtures in a row for the first time in 2017-18 than suffered another setback and it is really the story of their season.
It also ended Los Blancos' seven-match unbeaten run.
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The champions saw their five-game winning run in all competitions emphatically ended when Gerard Moreno slammed home a dramatic late victor for lowly Espanyol. Its last league win came eight rounds ago, at Levante. It's not just that Real Madrid are the reigning Spanish, European and world champions, more that Espanyol's record against them is so bad that Barcelona fans accuse Espanyol of lying down against their biggest rivals.
Espanyol had never beaten Madrid at RCDE Stadium, where it began playing in 2009.
Moreno threaded a attractive through ball to the right side to Sergio Garcia to start the play.
"We started the first half very well and had chances, but we failed to take them".
"We didn't deserve this defeat, it hurts".
Girona remained in the fight for a Europa League spot by defeating Celta Vigo 1-0 at home, continuing its impressive debut season in the first division.
The Catalan club were coming off a 6-1 loss against Barcelona at the Camp Nou.