Real Madrid crashed out of the King's Cup quarter-finals 4-3 on aggregate after being held to a 2-2 draw at Celta Vigo on Wednesday in another major setback for the stuttering European champions.
Real twice fought back to equalise on a rainswept evening in Galicia but it was not enough to save them from being eliminated in a knockout competition for the first time under Zidane who oversaw a Spanish record 40-game unbeaten run before successive defeats this month.
An own goal from Brazilian defender Danilo put Celta ahead in the 44th minute but Cristiano Ronaldo levelled for Real by lashing in a free kick from 28 metres in the 62nd.
Danish international Daniel Wass sealed Celta's place in the semi-finals with a shot from the edge of the area in the 85th minute before Real substitute Lucas Vazquez ensured a nervy finish by equalising with a diving header.
Real captain Sergio Ramos almost sent the tie into extra-time when he headed Toni Kroos's whipped free kick inches wide of the near post but Celta hung on.
Real have now failed to reach the Cup semi-finals for the last three years, losing to Atletico Madrid in the last 16 in 2015 and suffering a humiliating expulsion from last year's competition for fielding an ineligible player.
"We came very close, we had a fantastic first half an hour but then everything changed with Danilo's own goal. We're not going to look back we're going to only look forward, but if we keep playing this week with this character and personality we'll keep progressing," Zidane told Gol Television.
"There's no remedy for this other than to go all out for the league and the Champions League," added the French coach, whose side top the La Liga standings by a point with a game in hand on rivals Barcelona and Sevilla.
Celta, who have reached three King's Cup finals but never lifted the trophy, made the last four for the second year running and are targeting a first appearance in the final since 2001.
"We deserved a really happy moment like this, eliminating a rival like Real Madrid is not easy and it was great to see how happy the fans were," Celta captain Hugo Mallo said.
Earlier on Wednesday, Atletico Madrid reached the semi-finals for the first time in three years after coming from behind to draw 2-2 at Eibar, advancing to the last four 5-2 on aggregate.
Jose Gimenez headed home from a corner in the 49th minute to put Atletico four goals up on aggregate following last week's 3-0 win at the Vicente Calderon but Sergi Enrich levelled in the 73rd minute on the rebound after Pedro Leon had hit the post.
Leon's half-volley gave Eibar the lead in the 80th minute but the minnows still needed three goals to reach the semis and Juanfran's chip in the 85th confirmed Atletico's progress.
Atletico and Celta joined Alaves in the last four after the Basque side beat Second Division side Alcorcon 2-0 on aggregate on Tuesday.
Holders Barcelona will be looking to reach the Cup semis for the seventh consecutive year when they host Real Sociedad on Thursday having won the first leg 1-0.