Real, bidding for their first La Liga title since 2012, lost 2-1 to Sevilla on Sunday, conceding two goals in the last five minutes to leave themselves one point clear of Sevilla at the top of La Liga and two ahead of Barca.
"It won't affect anything," Zidane told his club's website.
"We knew that the run would come to an end at some point. I'm very proud of my players and the 40-game unbeaten run."
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Since losing 2-0 to Wolfsburg in the Champions League last season, Real had won 30 matches and drawn 10, scoring 115 goals.
Then came Sunday's painful reverse, which started with an own goal from former Sevilla defender Sergio Ramos and was followed by Stevan Jovetic's strike two minutes into stoppage time.
"We're hurting after the defeat," Zidane said. "We need to channel this defeat because nobody likes to lose, especially in this manner.
"But that is football and now we've got to rest up."
Ramos remained upbeat following his blunder, particularly as Real have a game in hand on all their rivals.
"Destiny is still in our own hands, we're still top," he said. "We face the steepest mountain of them all and it's a case of seeing who gets to the top first and who's able to hold on in there."
Real, who have also reached the last 16 of the Champions League which they won last year, host Celta Vigo in a King's Cup quarter-final first leg on Wednesday before playing Malaga in La Liga on Saturday.
(Reporting by Adriana Garcia, editing by Ed Osmond)
