Madrid lost for the first time since October as the side from San Sebastian triumphed 4-3 in the Santiago Bernabeu after leading 4-1 with just over 10 minutes remaining.
Zidane's team now travels to play Osasuna in the El Sadar stadium, where Madrid traditionally get the most hostile receptions of the season and where Osasuna have only lost two times all campaign, but the coach backed his side to react.
"We know what sort of a game we are going to have. It is a difficult game against a tough rival that is doing things well," he commented, according to Xinhua news.
Zidane made seven changes to his usual starting 11 on Thursday and players such as Casemiro, Raphael Varane and Ferland Mendy will all return on Sunday, with others such as Marcelo stepping down.
Marcelo came in for heavy criticism on Thursday after another poor defensive display, although the coach defended the Brazilian.
"The main thing is that we give everything on the pitch...We went 21 games without defeat," he said, although he admitted he was "not happy" about the Cup exit.
"In the other 21 games we won, I always said we hadn't won any titles, and nothing is changing because we lost one. We have to fight until the end of the season. We have a game on Sunday and another next week. I am not going to change anything," commented Zidane.
Thibaut Courtois will be back in goal on Thursday, while Eden Hazard and Gareth Bale will probably also return after their respective ankle injuries, although both will probably start on the subs' bench.