Neville has endured a gloomy first foray into management with his side slipping to 14th in the table having failed to win a single league match in nine games since the former Manchester United and England defender took over in November.
Calls from disgruntled fans for Neville to step down have increased in volume since the club suffered a humiliating 7-0 defeat to Barcelona in the first leg of their King's Cup semi-final last week.
Neville, however, says he is remaining calm and focussed ahead of Saturday's home clash with Espanyol.
"I haven't seen the players panic and they've not seen me panic," he told a news conference on Friday.
"There can be a hurricane on the outside but you have to be in the eye of the storm on the inside."
Valencia, who won two La Liga titles and reached back-to-back Champions League finals at the start of the previous decade, have not finished outside the top 10 in the league since 1988.
They face an Espanyol side on Saturday who are below them in 17th in the table and Neville has called on fans to rally behind their flailing team.
"We have to win against Espanyol and that's what we're focusing on. It's a final," he said.
"I am grateful to the fans who came out to support us," "Those who didn't want to come are within their rights...
"We need the fans more than ever on Saturday."
(Reporting by Toby Davis in London,; editing by Pritha Sarkar)
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