It was a former Manchester United teammate of Neville's that did the damage at the Estadi Ciutat de Valencia, with Giuseppe Rossi scoring the game's only goal in the second half.
The hosts dominated much of the opening 45 minutes, but they were unable to find a way past Diego Alves in the Valencia goal.
However, the Brazilian keeper was eventually beaten in the 65th minute by what turned out to be the winning strike.
The visiting defence failed to deal with a long throw into their box and when the ball broke for Rossi, the Italian frontman buried his volley into the bottom right-hand corner of the net.
It was a muted response from Neville's men, who have now lost 10 of their 29 La Liga matches this term and currently sit 12th in the table.