Gary Neville insisted he would not resign after Sunday’s 2-0 defeat by Celta Vigo prompted chants from Valencia fans for him to leave but his time at Mestalla will not now extend beyond the end of the season unless there is an unexpected turnaround.

A meeting with the club’s owners has been pencilled in for April but both parties are aware that there are few reasons for his five-month deal to be extended. It is not just a case of Valencia’s willingness to offer Neville a new deal but also that the Englishman, aware that results mean he has not earned it, will not demand one.

Neville’s relationship with the club is fluid, with regular communication between the coach and the club’s president, Layhoon Chan, and owner, Peter Lim. The owner is a friend and business partner of Neville’s and their mutual respect means there is a willingness to find the best solution by everybody.

The front page of Super Deporte after Valencia’s 2-0 defeat to Celta de Vigo. Photograph: www.superdeporte.es

On Sunday evening fans at Mestalla chanted “Gary, vete ya!” (Gary, go now!) in significant numbers for the first time. Valencia have won only three of 16 league games under him and are six points off the relegation zone. The fans’ fury was increased by Neville’s decision to replace Rodrigo and Paco Alcácer. “Gary, vete ya” was splashed across the front page of the local sports newspaper Super Deporte.

After the game Neville said he would not be joining up with England on Monday as initially planned and as stipulated in his contract. Instead, aware that his departure now amid the crisis of results is a sensitive subject, he will wait until Thursday. “I have just spoken to Roy Hodgson and I am going to stay back in Valencia; I feel it’s the right thing to do,” he said.

“Obviously its not an ideal situation, in respect to the fact that before I came here I was the assistant coach for the national team of England, with 60 million people, but I understand the two or three million people in Valencia need my attention this week. The last thing I want is for people here to say Gary Neville lacks commitment, because it’s not something that’s even been said about me in my life.”

Neville’s decision did little to change the situation, though. It may even have made things worse. The Valencia reporter for Onda Cero radio called it a “lack of respect”, while in AS it was described sarcastically as “English humour”.

After the club’s Europa League exit last week a poll in one local paper asked what Valencia needed to do next. As the early results came in, 0% had gone for “sack the manager”, while 67% voted for “begin a revolution in the squad”. But judging by the Mestalla on Sunday night, opinion is shifting against him.

It is two months since Neville rejected suggestions that the supporters were against him, insisting: “They have a very fine way of telling you when they are asking you about your position.” Now, they have. The chants were widespread on Sunday and at Valencia’s Paterna training ground the following morning two supporters waited with a banner that read “Gary resign” in English.

Neville has no intention of doing that at the moment. The end of the season is a different matter, though. Neville has insisted he has come to love the club and the city and that he would like to stay but that outcome is unlikely.

The former Manchester United full-back has refused to say explicitly that he will leave. He has talked simply about seeing out the final weeks of his short-term contract. Unless there is a significant and unexpected change or if the club’s owners can persuade him to stay, he will depart in the summer. Asked last Thursday if he was definitively ruling out an extended stay, Neville said: “No, I’m not closing the door. All I’m saying is that I know that the contract I was given was for five months – you know what my contract was. I knew that it was five months and that I had to get results.”

Valencia have not got them. The only thing they have to play for now is survival. After Sunday’s defeat Neville said: “The results have not been good enough. I’ve been very clear about that. I’ve got to concentrate on the games we’ve got left get to the end of the season. I was brought here for five months and accepted the huge challenge that exists. My point of view is that the results have been nowhere near what I expected, nowhere near good enough.”