"It's very hard for the confidence", said head coach Zidane, who guided Madrid to UEFA Super Cup, Supercopa de Espana and Club World Cup glory earlier in the season.
Zinedine Zidane's Los Blancos went into their league clash on 32 points - 16 adridt of pacesetters Barcelona - and that's where they remained after a sublime finish from Pablo Fornals finished off an 87th-minute counter-attack from the Yellow Submarine.
Atletico survived a stoppage-time scare when Augusto Fernandez handled the ball during a goalmouth scramble but went unpunished by the referee.
Valencia won 2-1 at Deportivo La Coruna to move up to 40 points.
"We didn't deserve this result".
The news source, Marca is reporting that the Real Madrid hierarchy have total confidence in the Frenchman.
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Gareth Bale had a goal disallowed for offside early in the first half.
"It is how it looks from the outside - we are sad, angry and we feel like we are sinking", added the Brazilian fullback. "This is a bad spell, nothing more".
Los Blancos are struggling this season, having dropped 19 points behind their bitter rivals FC Barcelona, while Cristiano Ronaldo is failing to shine in LaLiga with just four goals this campaign so far.
The Portuguese was livid with the referee, as he thought that he was tripped by Daniele Bonera just before he shot.
Asenjo made a number of more routine saves in the second period before the visitors cleared a late Real corner and set Denis Cheryshev clear down the left.
Fornals clipped home his 87th-minute victor just after it looked like Enes Unal had fluffed his team's chance to snatch the three points after a blistering counter-attack following a Real Madrid corner.
The goal came after a great save by Madrid goalkeeper Keylor Navas following a counterattack.
"There are always hard times during the season, which is what you're trying to convey, but I don't think like that".