Marco Asensio scored twice as Los Blancos came from behind late on to draw with Valencia in the entertaining La Liga clash.
Los Blancos refused to be beaten, however, and Asensio levelled the scores with a free kick in the 83rd minute.
Karim Benzema missed three excellent chances to win it for Real Madrid late on, but Zidane has insisted that he is "very proud" of his players for the effort they put into the match.
"I can't be happy with the result because we played an excellent game and deserved more," Zidane told reporters. "But you cannot always win. I am very proud of my players and that is most important.
"We only lacked finishing. We had seven or eight clear chances and did not score, so the game was there [to be won]. We need to continue like this and think about the next game."
Next up for Real Madrid is a home game against Levante on September 9.