Despite a number of difficulties early on in the last campaign the Toffees finished seventh, eight points adrift of Tottenham who claimed the final Europa League spot.
With the squad now in full training at their pre-season camp in Austria, Neville has renewed optimism about getting back into continental competition.
"We finished seventh last term when everyone thought we were average," the captain said in a webchat on the club's website.
"My aim this season is to get Everton back into Europe."
Asked about what winning a trophy - the club's last was the 1995 FA Cup - would mean to him, the former Manchester United player added: "It would be right up there with the best things I have ever achieved."
Source: Team Talk
Source: Team Talk