Zidane's men hadn't lost in a Spanish record 40 games stretching back to April last year before conceding twice in the final five minutes to lose 2-1 at Sevilla on Sunday.
And Zidane believes the European champions suffered a hangover from that disappointment in a first 45 minutes devoid of goalmouth action at a frigid Santiago Bernabeu with temperatures plummeting below zero degrees
"It was a strange game, especially the start," said Zidane.
"We have to analyse it, something is wrong for sure. We didn't do what we had prepared to do, especially the intensity. The intensity wasn't good at the start of the game."
However, the real damage to the hosts was done in a six-minute spell midway through the second-half as Celta grabbed two vital away goals and their first win at the Bernabeu in a decade.
Iago Aspas's 15th goal of the season put the visitors in front before Marcelo equalised with a sensational volley five minutes later.
However, Celta went immediately back in front when left-back Jonny exploited a huge gap in the centre of the Madrid defence to slot home.
The sides meet again for the second leg on January 25.
"There is no excuse. We are Real Madrid," added Zidane.
"We have to keep working and think about the next game. We will overcome this.
"We have done well until now and in the last two games we can't be happy with above all the results. The performance in Sevilla was good, today it was a bit worse, but we shouldn't worry."
However, Brazilian midfielder Casemiro admitted Real's confidence has been rocked by back-to-back defeats.
"This defeat is concerning because Madrid can never lose," he said.
"Losing in Seville has damaged us."
Celta boss Eduardo Berizzo claimed he wasn't surprised by his side's success having knocked Atletico Madrid out at this stage of the competition last season.
However, he insisted Madrid remain the favourites to progress and believes Celta will need to play even better in the return leg in seven days time to reach the last four.
"It is a bit arrogant to say we are favourites against Real Madrid, but we will enjoy a win like this," said Berizzo.
"None of my team's victories surprise me. It is a huge win, coming to a place like this and facing the best team in the world, but we believed we could do it.
"We are happy to win, but it obliges us to play even better in Vigo because we are facing a brilliant opponent and it is the toughest footballing test."