And the Goodison skipper accepts the time has come for David Moyes's side to start winning at the homes of the Premier League's top four teams.
Everton slipped to a 1-0 defeat to Liverpool in Saturday's 213th Merseyside derby despite playing almost an hour with an extra man following the 34th-minute dismissal of home centre-back Sotirios Kyrgiakos.
It brought the Goodison outfit's nine-game unbeaten league run to a shuddering halt and means they still have not won at their neighbours since September 1999.
Indeed, that triumph was Everton's last at one of the supposed 'big four', a run that now stretches to a remarkable 48 games.
Neville said: "It's definitely a big chance missed. Before the game we were confident and when they went to 10 men you think to yourself 'it's going to be our day'.
"But maybe that was a bad thing for us because they knew they could sit back and we had to try and force the play.
"We had the team to play but when they went to 10 they obviously had a cause to fight for and it galvanised them and the crowd.
"The goal gave them something to hang on to, but apart from a couple of times when we got behind them, we didn't stretch them enough."
Although soundly beaten at Manchester United earlier in the season, Everton earned a 3-3 draw at Chelsea in December and were only denied victory at Arsenal last month by an injury-time equaliser.
Moyes's side host Chelsea and United in their next two games of a testing February, but Neville believes it is on their travels against the Premier League's upper echelons that Everton must begin producing.
"We need to start winning away to top four sides," he said.
"We had an unbelievable opportunity at Arsenal and threw it away in the last minute and this was another chance. We've gone to top sides and got draws but want the next step now. We're getting more belief we can come to places like this and win, though. The gap (between Liverpool and Everton) has been closing for a couple of seasons and our performances have definitely been getting better.
"We seemed so near, but the final step is always the hardest and it's one we are striving for. I don't think it is a psychological thing, we just needed that bit of quality.