The former England and Manchester United defender was brought in to put the club back on track after a slow start to the season but they are yet to win under him in three La Liga games.
Two draws and a defeat have left them 10th in the table after 17 matches, 11 points adrift of Villarreal who occupy fourth spot, the position that earns qualification for the preliminary round of the Champions League.
Valencia also face a severe test against third-placed Real Madrid on Sunday.
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"It is a large distance to make up and I am concentrating on the next game," Neville told a news conference. "The defeat makes it a lot more difficult but there are still points to be played for.
"I am desperately looking to pick up points but I am also looking for a good performance. There were good signs against Olympique Lyonnais and Eibar but today we saw something different as we had a good 45 minutes.
"This makes me feel better as we knew how to play in the second half and if we continue that way then it is possible to pick up the points we need. In the second half we played the best football since I arrived," added Neville.
Valencia began very defensively against Villarreal with a five-man rearguard and, although they came out of their shells after the break, conceded from a Bruno Soriano free kick in the 64th minute.
"We needed to pass the ball better. We were bunched together too much and we should have looked to attack more," said Neville.
"When you have five at the back you can be too defensive and we were conscious of that but we didn't do it well."
(Editing by Tony Jimenez)
