The League One side made the Merseysiders pay for a host of missed chances by taking the Carling Cup tie 4-3 on penalties after the scores were level at 1-1 after extra time on Wednesday night.
The defeat is yet another blow for David Moyes' team, whose only win of the campaign so far came in the previous round against Huddersfield.
Defeats against Blackburn, Newcastle and Aston Villa have left the Toffees second from bottom of the Barclays Premier League in a season where Moyes was expected to lead his side back into Europe.
Neville, who has been restricted to two appearances this year due to injury, has told his players to forget about Europe and realise that their immediate priority should instead be to claw themselves out of the relegation zone quickly.
"There are no excuses. No hiding places. We don't deserve to win these football matches at the moment," Neville told the Liverpool Echo.
"We didn't win at Blackburn - hard luck. We didn't win at Wolves - hard luck. We couldn't beat Villa - hard luck. Everyone says we're playing well but not winning games. Forget all that rubbish now - it's got to the point where it's time to realise where we are.
"Forget Champions League football, forget Europa League football. Focus on Saturday and just winning. Maybe at the start of the season we looked at the end of the season rather than concentrating on the now."
Saturday will be the first chance the Toffees have of ending their dismal start to the season when they take on Brentford's neighbours Fulham.
The Cottagers' chances of extending their impressive start to the season took a blow last night when striker Moussa Dembele was injured during their Carling Cup defeat to Stoke.
With key strikers Bobby Zamora and Andy Johnson also sidelined, the clash gives Moyes' team a good chance of picking up their first league win of the season.
Moyes, however, insists his own strikers must first find form if the Toffees are to kickstart their season.
Jermaine Beckford, Louis Saha and Yakubu have all struggled in front of goal for Everton, who are yet to score away from home this season.
"We just haven't been clinical enough at the other end," said Moyes.
"We should have put it out of sight within 20 or 30 minutes. We had lots of chances early on."
The Scot admits that he is worried about Everton's form and takes full responsibility for the slump.
"I am concerned. Any manager in that position would be concerned," Moyes said.
"It has been a bad start to the season but it's my job to get managing and get things turned around."
Brentford manager Andy Scott, who hailed last night's win as the biggest of his managerial career, is confident that Moyes will turn around Everton's fortunes.
"David gets credit every year for being a fantastic manager every year and he deserves to," Scott, 38, said.
"The way he sets his side up and the way he plays, the way he does things is really a model for people like myself. He'll turn it around and they'll get their league form going."
Source: Team Talk
Source: Team Talk