Alvaro Garcia Pascual struck the winner just after halftime to secure Sevilla's Primera safety.
Caparros said afterwards: "A very intense game. The first thing I want to say is that our fans are spectacular. They showed they're centuries old, that they know they have to support the team regardless of the social situation. The colour was spectacular. Bravo. Top marks.
"I take my hat off to our fans and the players. When there's a negative situation, when our lives are on the line, it's not easy. The players came out, gave everything, and we had chances. We suffered, but we got an important victory for Sevilla."
The players said 'this is the game'
On the players, he also stated: "I told them before the game. We've worked, we've seen where we can hurt Las Palmas, our strengths... But the coach was already unnecessary. They said 'this is the game'."
Caparros added: "We've all suffered, my whole family, like all Sevilla fans. I haven't suffered more, I've suffered the same.
"The sad thing is, when I come to Sevilla, not having been the catalyst people expected. Thank God we've achieved it, I'm happy, and now we have to prepare for the next game."