"OK, I'm a bit cross. Of course I'm cross," the Spaniard told a post-match news conference.
"Football is not just about keeping the ball. We want possession to attack. We did not have sufficient space but we did have sufficient possibilities to score goals," he said.
Spain often monopolised possession but a compact Swiss defence pushed the talented European champions onto the flanks and they lacked punch in front of goal until Del Bosque brought on three attackers in the second half.
Substitute Fernando Torres, returning to the side after knee surgery, had a string of chances as Spain frantically pushed for an equaliser but he blasted the best opportunities over the bar or wide of the target.
"We tried to use Torres as another attacker and we had possibilities, but they defended very well, all the balls coming along the lines were stopped very efficiently," said the coach.
Del Bosque rejected suggestions he should have played more strikers from the start, rather than just the diminutive David Villa as a lone frontman against the towering Swiss defence.
"I respect all opinions. We have been playing our style for quite some time, and it has proven successful so far," he said. "We had corner kicks, we had set-pieces, we could have scored, but today was not our day."
Spain came into the game on the back of 12 straight victories and had never lost to Switzerland in previous 18 games stretching back to 1925.
Spain now face Honduras and Chile and must be hoping Switzerland slip up as the Group H runners-up will face the winner of Group G - which includes Brazil, Portugal and Ivory Coast.
"Somebody had luck against Spain today and the amazing thing is that they might have scored another goal after that first goal," said Del Bosque.
"We must really give everything, we cannot stand there simply our heads hanging thinking we're just unlucky chaps. No, we're going to fight for it, we'll be good.
"Today we had an obstacle and we will overcome it in the next two matches. But nobody has spoken about winning the World Cup, nobody has spoken about the final because this is not how football works."
