It has been a bleak summer for the Merseyside club and chairman Bill Kenwright has admitted a dire financial situation has been behind a lack of transfer activity.
Everton also lost their Premier League season-opener against last season's Championship winners QPR on Saturday following the postponement of their first match at Tottenham.
Next up is a difficult looking Carling Cup tie against League One Sheffield United on Wednesday and captain Neville is demanding improvements.
"It wasn't good enough," said Neville after Saturday's defeat to QPR. "I think this is important to say. We can't beat around the bush.
"There feels as if there is a lot of negativity surrounding the place at the moment and everyone can feel it. I think it is important to say that there are a lot of good things happening here.
"We have got great foundations, great supporters and a set of players that have done really well these last three or four years.
"Supporters will say it is easy for me to talk about the spirit of the club but the spirit is what has set this club apart, going back to the days when Howard Kendall was manager and, before that, when Brian Labone was playing.
"Now we need that spirit more than ever. We have got a lot of good things going on and we can't let these things outside destabilise us.
"We have not spoken about getting off to a great start to the season. We did that last year and it never happened. We failed today (Saturday). As a group, we didn't play well enough and we are all disappointed.
"We all take responsibility and nothing off the pitch has interfered with our preparations. We had a great pre-season, everything was spot on. We didn't perform but the motivation is there for us. Our reputations are on the line and we have got to perform."