Spain sacked head coach Julen Lopetegui after he was named the new Real Madrid boss - two days before their opening World Cup match against Portugal.
Real Madrid announced on Tuesday that Lopetegui would succeed Zidane at the Bernabeu on a three-year deal.
The Spanish football federation (RFEF) said it had dismissed the 51-year-old because the negotiation occurred "without any information to the RFEF".
"I know it's a very difficult situation. I know there's going to be criticism whatever I do," said RFEF president Luis Rubiales, who was told of Lopetegui's new role five minutes before it was announced.
"I'm sure this will, in time, make us stronger. I admire Julen very much, I respect him very much. He seems a top trainer and that makes it harder to make the decision.
"You can't do things this way, two or three days before the World Cup. We have been compelled to make this decision."
Lopetegui became Spain manager in 2016 following Vicente del Bosque's retirement, and remained unbeaten through his reign.