After Alvaro Odriozola scored his maiden international goal with a sensational volley, Spain looked on track to win their first friendly ahead of Russia 2018.
But a shot from Swiss captain Stephan Lichtsteiner was spilled by De Gea, allowing Ricardo Rodriguez to tap in from close-range.
Spain remain unbeaten in the 19 matches since Lopetegui was appointed following Euro 2016 and the coach will make no rash decisions in the wake of De Gea's error.
"David knows that I know he's going to take us forward in many games and I have no doubt [about him]," Lopetegui told reporters after a 1-1 draw in Villarreal.
Spain have one more warm-up game scheduled before opening their World Cup campaign with a derby clash against Iberian neighbours Portugal.
But with next Saturday's match against Tunisia taking place in Krasnodar, this weekend's game at Estadio de la Ceramica may have been the last time former Barcelona captain Andres Iniesta represented Spain on home soil.
Iniesta was substituted early in the second half to a standing ovation after shaking off a bang to the knee sustained in a challenge with Switzerland striker Breel Embolo.
"The ovation has been won by the performance of his entire career," Lopetegui added of Vissel Kobe's new signing.
"But the most important thing is the match he has made, showing his absolute validity.
"We are in the preparation phase and we were thinking of replacing him. What matters most to us is what he is still about to give us.
"I liked that we were able to generate a lot of chances against a complicated team like Switzerland.
"We have maintained a very high level, we had to adjust some things at the break, but in general we have many positive things, no injuries and we continue preparing to arrive in perfect condition to the World Cup."