Lucas Perez and Joselu scored on either side of the half for Alaves, and Madrid could only respond with a late Casemiro consolation in the 86th minute.
Madrid have now lost three of their last five home games in all competitions, as many defeats as in their previous 31 matches at home.
To make the night even worse, Eden Hazard's injury woes continued as the Belgian was taken off in the first half.
"I don't have an explanation," Zidane said. "Tonight we alternated good moments with bad moments. When they scored a goal after three minutes, things get very complicated for us.
"The other day in Milan we played a good game and today...It is reality, our reality today. What we have to do is keep working, recover players and change the dynamics. We don't have consistency."
When asked what he would say to his players to help them gain more consistency, Zidane replied: "I have to find the solution with the players. I am not going to say it here. We must not only think about the negative. We also have to see what we did well and try to be more consistent."
Zidane was particularly dismayed by his side's start, as Alaves earned a fifth-minute penalty when Victor Laguardia's header struck Nacho on the upper arm. Perez would put home the ensuing penalty to give the visitors an ideal opening to the game.
"It's the worst start of the season," Zidane admitted. "We couldn't change the dynamics of the game and that bothers and worries me."
Madrid will face another quick turnaround as they now travel to face Shakhtar Donetsk in the Champions League on Tuesday.