A Madrid side showing 10 changes from their last outing held on for a 2-1 victory, lifting them to within a point of Atletico Madrid in second, but Zidane was not entirely pleased with what he witnessed at the Bernabeu.
"I was angry with myself today, for some things, but not with the players," he told reporters at his post-match press conference. "I am happy with the attitude of my players, it has been exemplary.
"The first half was phenomenal. We cannot be happy with what we have done in La Liga because we lost many points at the beginning."
Real return to action on Tuesday night with the second leg of their Champions League semi-final against Bayern Munich, which they lead 2-1.