A 2-2 draw on the night at Balaidos saw Celta progress to the semi-finals 4-3 on aggregate as Zidane's men have now failed to win in three of their last four games following a Spanish record 40-match unbeaten run.
"I am not worried, nor angry," said the Frenchman. "Lately we've chances that we haven't taken, that will change."
Just as in Saturday's 2-1 win over Malaga both Real's goals on the night came from set-pieces.
However, Cristiano Ronaldo's stunning free-kick and Lucas Vazquez's injury-time header from a corner weren't enough as Celta twice went in front on the night through a Danilo own goal and Daniel Wass's calm finish five minutes from time.
Zidane, though, rejected the claim that his side lack creativity, particularly with Luka Modric and James Rodriguez sidelined by injury.
"It is true that we didn't score from open play. There were two more goals from dead balls, but tactically we played a great game," he added.
"My sensation is that we played very well and that we pushed the opponents all the way to the end."
In total Madrid were missing seven first-team regulars with Gareth Bale, Marcelo, Dani Carvajal, Pepe and Raphael Varane also out.
However, Vazquez believes it is unfair on those who came into the side to claim they were badly missed.
"We have shown throughout the whole season that whoever comes into the side responds," the Spanish international told GolTV.
"Perhaps it is a bit opportunistic to say that today we missed the absentees."
By contrast, Celta are now just three games away from landing a first ever major trophy.
Celta boss Eduardo Berizzo's decision to make eight changes at the weekend in a 1-0 defeat to Real Sociedad to ensure his players were well-rested proved justified as the hosts withstood a second-half onslaught.
"The players were capable of knocking out a giant like Real Madrid," said Berizzo.
"We knew we would have to suffer. Madrid oblige you to have an almost heroic game in defence.
"Then when you have the chance to do them damage, you have to take it.
"I want to thank the fans for their support. The strength we feel together allows us to look to the future with excitement."