The defeat was Spain's first on home soil in almost four years and dampened their chances of reaching the Nations League finals next year.
La Roja now find themselves two points behind leaders Portugal going into Tuesday's final game between the two sides.
Manuel Akanji's first half header gave Switzerland the lead but Jordi Alba equalised with Spain's first shot on target in the 55th minute before Breel Embolo won it for the visitors just three minutes later.
"Losing is always something that hurts. It has been a pity, but we must value Switzerland, who from the beginning caused us many difficulties," the coach said.
"In the first half, it was the worst of my time as coach. [Then] we have badly defended the corner of their second goal.
"In the second half we improved. We have tried until the end. The key game is Portugal. We will go to Braga to win."
Asked if the defeat generated doubts in relation to Qatar 2022, Enrique replied: "No doubts.
"Obviously it's better to go to Qatar on a winning streak, but I have full confidence in the team. I have seen many players in the first half who have been more imprecise than ever, but the opponents are good, they know how they play.
"But everything doesn't always go well, when you don't have a good day, this happens.
"A victory against Portugal would be the perfect way to reach the World Cup. We have drawn three times with them and now we will go there to win."
