Appointed last month to replace the sacked Nuno Espirito Santo, Neville has presided over three draws and two defeats in La Liga, as well as seeing Valencia eliminated from the Champions League thanks to a 2-0 loss to Olympique Lyonnais.
They are mired in mid table in La Liga at the halfway stage of the campaign, well short of the European qualification places that the ambitious Singapore-owned club expect to be challenging for.
Neville told a news conference he wanted the Valencia supporters to understand what the team was trying to do and continue supporting the players while admitting they had squandered possession to the Basque club far too often.
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A late Jonathas double secured victory for Sociedad with Valencia's best moment coming in the first half when a Rodrigo Moreno effort hit the crossbar.
"Everyone in the dressing room is disappointed, myself more than anyone, but tomorrow everything starts again," the former Manchester United and England defender said.
"I can't sit here without saying it's not a blow," he added.
"We lost against Villarreal (last month) but I was happy with our second-half performance.
"Today I can't say that. We played below expectations and we have to start winning regularly."
Neville reiterated that bringing in reinforcements in the January transfer window was not necessarily the answer.
"I want to play with these players so they can improve together," he told reporters.
"It's not that the club doesn't want to spend money. There have been some important signings and my job is to get the players to perform.
"I believe I have some excellent players and I assume responsibility for the defeat."
Valencia play the first leg of their Europa League last 32 tie against Rapid Vienna next month and are well placed to reach the quarter-finals of the King's Cup.
Their next outing in La Liga is at home to struggling Rayo Vallecano next weekend.
(Writing by Iain Rogers, editing by Toby Davis)
