Juanlu Sanchez scored twice, with Isaac Romero and Dodi Lukebakio also on the scoresheet.
Garcia Pimienta said afterwards: "We said before the game that it was a very demanding game. It's true that it's against the bottom team, but if we hadn't taken the game seriously , as we did, it would have been very difficult, if not impossible, to win here. We were a very practical team, very solid defensively, conceding very little , playing well and having very clear chances at goal. We were effective in a way that we haven't been on other days.
"We were focused and conceding very little. This victory also shows us the way forward a bit . If we're this solid it's difficult to beat us and we have a chance of winning. I'm happy with the victory, the lads deserved it, but especially the fans. A thousand Sevilla fans travelled to Valladolid cheering the team on at all times and this victory is for them."
On Juanlu's game, he said: "We are at Sevilla and there are great players. It is true that his ideal position, so to speak, would be winger, inside midfielder, wing-back, full-back... That is where I think he performs best, but playing inside gives us a lot of energy. He is a player who can get through from the second line a lot.
"He has scored two goals. In the first half he hit the post. Apart from playing well, he gives us a lot of work. I am happy for him and for the reward of the two goals, which strengthens you a little more."