The Frenchman had overseen two wins since stepping back into the Real hotseat following the sacking of former team-mate Santiago Solari last month but Valencia were his first acid test.
Los Che had been unbeaten in La Liga since January 5 and they extended that run thanks to goals from Goncalo Guedes and former Real defender Ezequiel Garay, with Karim Benzema's header in injury-time scant consolation.
Zidane said in quotes on Real's official website: "We started the game strongly with good possession, pressing high up. We just needed to get that first goal.
"I can't blame the players for anything, they really tried hard. We played against a top team. It's a defeat and defeat always hurts. 'We struggled to create chances, get shots off and come up with anything in the final third. We needed a little bit more near the opposition goal.
"The team fought to the end. It's a tough spell, a defeat, but we have to accept it and think about the eight games we have left. We have to focus on doing a better job on Saturday."
Valencia trio Kevin Gameiro, Geoffrey Kondogbia and Rodrigo all missed the target when well-placed while Real struggled in the final third.
Zidane, though, feels his side competed on equal footing with their opponents after watching them slide to their ninth league defeat of the season.
He added: "I always say results are fair and I accept them but it was an even game. They got two goals against us almost out of nowhere. We have to accept that Valencia won the game.
"This is a tough run for us, the whole season has been hard going.
"Now I need to take control of my team and get us playing better next time out. The players are ready to fight until the last and we want to end on a high in preparation for next season. We are going to leave no stone unturned."
Valencia head coach Marcelino felt his side were worthy of the three points.
Speaking in quotes published by his side's website, he said: "Real Madrid dominated us in the first minutes when we lacked precision, but we always had control of the game.
"I think we were very superior to Real Madrid and my feeling is that, due to the chances we had, the scoreline should have been greater."
Victory pushed Valencia to within a point of fourth-spotted Getafe and possible Champions League qualification for next season, though Marcelino was unwilling to get carried away.
He added: "As for the final stretch of the season, we are not favourites for anything, we must remain the same with this equality, work and humility.
"The calendar is very difficult and all the matches are going to be complicated. We are very satisfied with the level of play. If we do not have injuries, we will be closer to achieving the goal of the Champions League."