Goals from Dani Parejo and Santi Mina saw Valencia claim a 2-1 away win at Granada in La Liga on Sunday - adding to Thursday's 6-0 triumph over Rapid Vienna in the Europa League and last Saturday's 2-1 league victory at home to Espanyol.
The latest win saw Valencia secure back-to-back victories in La Liga for the first time since November, easing the pressure on Neville.
And after seeing his team win three games on the bounce, the former Manchester United player believes confidence is starting to return at Mestalla.
"It's a very important victory. You have to make the most of the good moments when they arrive, and the mood of the dressing room has changed," he said.
"We have to continue taking the victories; you can't get carried away, we must continue working in order to keep winning.
"I am not liberated by this win - I'm happy. We could have finished the first half 2-0 up, as we had two good chances.
"In the second half Granada were obviously going to press us a lot. We saw that this team never stopped believing."
Neville also confirmed Tunisian defender Aymen Abdennour is not far away from returning after suffering a hamstring strain in the side's win over Espanyol last Saturday.
"We now have a full squad available and Abdennour will be back very soon," he said.
"We have to keep changing the team because we have a very strong squad."
Valencia travel to Austria for the second leg of their round-of-32 tie against Rapid on Thursday before a home clash against Athletic Bilbao in La Liga on Sunday.