Spain-born Achraf Hakimi - one of 14 foreign-born players in Morocco's 26-man squad - dispatched the country of his birth with the winning penalty in a 3-0 shootout victory following a goalless 120 minutes.
The 52-year-old Enrique, who is now out of contract, said he could not complain about a performance in which his players carried out his instructions "to the letter".
"This is not the right time," Enrique said about his own future. "It's not relevant and it's not important.
"My contract is going to end but as you know I am very happy with the national team and the federation. I've always had great support from (sporting director Jose) Molina.
"I would always carry on but of course we need to think about what is best for me and what is best for the national team."
Enrique also shouldered the blame for Spain's penalty shootout exit.
"The responsibility is mine," he added. "I chose the first three penalty takers, who were those I thought were the best specialists on the pitch.
"We didn't even get to the fourth. Bounou is a spectacular goalkeeper in this aspect, he has a high percentage in going the right way. He was great."
"Football is a marvelous, passionate sport, but a team can win without attacking.
"Morocco attacked once or twice and were dangerous, but we dominated the game completely, and tried to create.
"We would have liked to create more. It was hard for us. We had 11 shots I think, but few on goal. In the final move of the game Pablo Sarabia hit the post. The penalty shootout was hard for us. But I'm proud of my players."