The Portugal forward then failed to convert a penalty before Dani Parejo equalised for Los Che with a 25-yard free kick, but Marcelo made sure of all three points when he drilled home four minutes from time.
"I am pleased with everyone's performance," Zidane told Sky Sports News. "Valencia kept playing their game and we couldn't find the second goal to kill the game off. We're going to have to dig in until the end.
"We weren't clinical enough right from the start, perhaps we're a bit anxious or tense, but we didn't let it get the better of us, we played our game and did a good job.
"If you don't finish the game off, you're going to struggle. Today we had chances to close the game out earlier, so that's something we can still improve on. It's true that we had half-an-hour when we slipped into our comfort zone, but that changed after the Valencia goal.
"The fans got behind us again after we conceded the goal and helped to drive the players on and there was a different feel to it. I can't explain the reason for it, but it is special to win it in the last 10 minutes, it is thrilling."
The result puts Real three points clear at the top of the La Liga table ahead of Barcelona's game at Espanyol.