Madrid struggled from the start, with Lucas Perez scoring an early penalty and Eden Hazard forced off injured, before Joselu doubled Alaves' lead in the second half, and Casemiro grabbed a late consolation goal.
"We played a bad game, above all at the start, and we couldn't change it," Zidane said. "I'm the coach and I take the blame, as always ... We have to move on from this. We have another game on Tuesday. We played really well against Inter, and today we didn't. There are no excuses. We shouldn't single out one player or another.
"We couldn't change the dynamic within the game and that annoys me. Right now, consistency is the problem we have. We've had a lot of injuries too. We don't look for excuses, but it's the reality. The game we played three days ago in Milan, and then today ... I don't have an explanation."
Hazard was substituted after just 28 minutes, with what early reports suggest is a thigh injury, and will undergo further tests on Sunday.
"Right now we don't know exactly what he has, " Zidane said. "I hope it's just a knock, as he said, and not a muscular injury. I hope so."
Hazard had only returned to action last weekend after testing positive for the coronavirus and before that was out for a month with another muscular problem.
His debut season at Real Madrid was heavily disrupted by injuries, with two ankle fractures restricting the Belgium international to just 16 La Liga appearances and one goal.
Their next two La Liga games are a tough away trip to top-four contenders Sevilla -- coached by former Madrid boss Julen Lopetegui -- followed by a derby with Diego Simeone's in-form Atletico Madrid.