Bruno Soriano’s sublime free-kick just after the hour-mark was enough to give in-form Villarreal the victory, leaving them firmly in with a chance of a top-four finish.
For Neville, it marked his first La Liga defeat in charge of Valencia, who face Rafael Benitez’s Real Madrid on Sunday.
Villarreal had the better opportunities in a first half lacking in decisive quality; Bruno forced Jaume Domenech into a good save after three minutes before the Villarreal captain put a free-kick inches wide of the left-hand post.
The game livened up in the second period, and Valencia had their first opportunity of the game as Andre Gomes’ effort was blocked from a corner from 15 yards.
Gomes then forced his way past two Villarreal defenders and found himself inside the area, but goalkeeper Alphonse Areola rushed out to block the midfielder from the angle.
Villarreal took the lead on 64 minutes through Bruno, who struck home a superb free-kick into the top left corner past Domenech after Roberto Soldado was fouled just outside the area.
Valencia could not find an equaliser despite some late pressure, leaving them 11 points off Villarreal, who sit in fourth place in La Liga.