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Sofiane Feghouli scored twice in the first half as the 10 men of Valencia defeated Rayo 3-0 at the Mestalla.
Valencia - fifth in the standings - had gone four league matches without a win before kick-off on Saturday.
"The three points from this game were vital for us," Nuno said post-game.
Article continues below"I am satisfied with how Rodrigo de Paul played, coming in for Dani Parejo.
"We played well, we scored goals and we created chances. We showed that Alvaro Negredo and Paco Alcacer can play together, along with Rodrigo, and whoever plays will depend on the game."
"All of our red cards this year have come when our player has been fighting for the ball and has been grabbed," Nuno added.
"The opposition player stops our man chasing the ball by holding him back, and we end up with a player sent off. I don't want to comment on refereeing, but I will say this: we are not a violent team."
