The victory at the Mestalla moved the European hopefuls into eighth position in La Liga, six points behind Villarreal with nine games remaining.
"Villarreal are a very good team, they're having a great season and we stood up well against them. In the end we have to suffer a bit, but I think we've responded very well at home and we're very happy with the result," he told VCF Play.
"We knew that our fans would get behind us, in such an important game against Villarreal. There's always a great desire to win a derby like this, not just from ourselves, but also from the fans and we were able to give them the win they deserved."
Next up for Valencia is a trip to Almeria on Thursday.