A 2-2 draw at Balaidos on Wednesday saw Madrid lose 4-3 on aggregate, with Celta reaching the semi-finals for the second season in succession.
Lucas Vazquez scored the visitors' second equaliser in the 90th minute after a Cristiano Ronaldo had earlier cancelled out Celta's 1-0 lead on the night, and one more goal would have sent Madrid through on away goals.
However, Celta held on for the aggregate win and Zidane says his team were just getting on top of their hosts when the referee blew for full-time.
"We played a great game," he told reporters. "We are disappointed but the boys played well and we ran out of time.
"Maybe if we played a few more minutes we could have won it. But it was not possible, we have to accept it and think about the league, which is next.
"I think with the game we played, all you have to do is relax and think that the cup is already far behind us and we have the league on Sunday.
Reflecting further on the Celta tie, Zidane added: "It's two games and we were not able to get through. We did all we could.
"What hurts is being knocked out after a performance like that because they [my players] do not deserve it.
"You blame yourself but there is nobody to blame really.
"The pity is that we didn't get what we expected. I am disappointed for the guys."