The Toffees are notoriously slow starters, but have bucked that trend this season to sit fifth in the Premier League table approaching the halfway stage.
The hectic festive programme will offer them ample opportunity to cement their lofty standing, while looking to push on into the UEFA Champions League places.
Neville claims that was the challenge put to the players by boss David Moyes before a ball was kicked, and he believes Everton are capable of surging into the New Year.
"I think we are doing really well," he told Sky Sports News HD.
"I think next week, when we play Wigan, is the turn of the year, is the halfway point, and if we can be in fifth or fourth position, that's where we wanted to be at the start of the season.
"That's the goal that the manager set us, be in the top four or be in and around the top four by the time we get to Christmas.
"After Christmas, that's where the league takes shape and we normally come good after Christmas. The second half of the season is where go up a couple of gears and I still think there is more to come from the team.
"We are playing well, we aren't losing many games, we are playing with confidence, playing good football, but I still think there is more to come."
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