Lopetegui was removed from his post after Real Madrid confirmed a day earlier that he would take over as their new boss after the World Cup.
He has since been replaced by Fernando Hierro for the duration of the competition. Hierro had served as Spain's sporting director since November.
Lopetegui was unsurprisingly crowded by reporters as he arrived at Krasnodar Airport but was unwilling to divulge anything about the saga.
"I hope we have a great World Cup," Lopetegui said. "I am not going to say anything else."
Spain begins its World Cup campaign against neighbour Portugal.