Zidane admitted that his players were affected by Madrid's unusual situation this season - eliminated from the Champions League and Copa del Rey and already out of the running in La Liga with a month-and-a-half still to play.
Despite picking up three points, Madrid really struggled against mid-table opposition and were spared embarrassment by their French striker, who scored the victor with nine minutes left.
Reflecting on the same, Zidane said that though Benzema has been scoring more goals in recent times, he has always been crucial for the club. "We will see. It is not the time to talk about this".
FW Karim Benzema, 8 - As so often this season, Benzema was Madrid's best performer and most likely source of a goal. "People's perception of him has changed as a result, but he's always been a crucial player".
Real Madrid are a staggering 13 points behind rivals Barcelona in the Primera Division, to whom they embarrassingly lost on three separate occasions this season. Barca and Atletico play each other later on Saturday.
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Benzema had two efforts ruled offside before he headed home twice in the second half, in nearly identical fashion, in the 59th and 81st minutes to give his side the lead. Marco Asensio did brilliantly to weave into space and dig out the cross.
The hosts had the ball in the back of the net after 11 minutes when through Bale's close-range strike, however the Welshman's effort was ruled out for offside. He netted a late victor for a 3-2 victory over Huesca last weekend and scored in a 2-1 loss at Valencia on Wednesday.
The Frenchman had two late chances to complete his hat-trick, missing an nearly empty goal after substitute Lucas Vazquez squared the ball for Benzema rather than taking the shot himself.