Goals in the first nine minutes from Simone Zaza and Fabian Orellana rendered Cristiano Ronaldo's reply just before half-time meaningless, and Madrid's advantage over Barcelona is now just one point – although Los Blancos have a game in hand.
Zidane stopped short of criticising his side's performance after the encounter, but he has warned against complacency as Madrid aim to clinch the club's first domestic league title since 2012.
"The truth is that we lost the match in 10 minutes," said Zidane. "We played well, we had opportunities but two errors cost us two goals.
"We had 80 minutes to get back in the game, we scored the goal, but we missed a lot in the second half and it's a shame.
"Now, of course, it will be even more difficult. We are still ahead but we have to think that this is not worth anything.
"No matches are won by going out to the field alone. The first 10 minutes have punished us a lot and we do not look for excuses."
Madrid had travelled to Mestalla hoping to add a fifth consecutive La Liga victory to their recent sequence, but Zidane believes the quality of his side's final ball let them down.
"We have lacked concentration," said Zidane. "We played too open, we must be more attentive.
"I do not think we were bad with the ball, but there is a lack of lucidity on the last pass.
"What we have to do is always be attentive and never lose concentration because they punish us. In the first 10 minutes we were not ready.
"Now, we think about Sunday's game and it's time to rest. We had a good chance to add to our lead but we have missed it."