Published: 2018-06-13 16:53:51 BdST
Real unexpectedly announced on Tuesday that Lopetegui, who had only recently extended his contract with Spain and was unbeaten in his 20 games in charge, would take over as their coach next season.
In announcing the decision, the head of the Spanish football federation (RFEF) Luis Rubiales said Lopetegui's replacement would be announced "soon".
Rubiales said the federation had found out about Lopetegui's move five minutes before it was announced by the Champions League winners.
"The coach, while he is a RFEF employee cannot do things in this way. I found out with a phone call five minutes before the official announcement. We feel obliged to take this decision," Rubiales told a news conference at the team base in Krasnodar.
"If anyone wants to talk to one of our employees, they have to speak to us, too. It's that basic. This is a Spain national team that represents all Spaniards, it's the most important team we have and the World Cup is the biggest stage of them all.
"I don't feel betrayed, the problem is that things have been done with the complete absence of the RFEF, which is something (we) cannot let go by."
Spain, one of the pre-tournament favourites and winners in 2010, also face Morocco and Iran in their group in Russia.
Rubiales added there were no hard feelings towards Lopetegui, who replaced Vicente del Bosque following Euro 2016.
"We want to thank Julen for all he's done and he's a big reason behind us being in Russia, but we feel obliged to dispense with his services," he said.
"There has to be a message to all RFEF employees and there are ways of behaving that you need to abide by."