Phil Neville, the Everton captain, has urged the club's board to back David Moyes in the transfer market this summer after claiming that it will be a “major disaster” if the manager is not given the funds to sign the “special player” that Neville believes can help them to gatecrash the Barclays Premier League's elite next season.

Everton secured a place in the Uefa Cup for the second successive year on Sunday after beating Newcastle United 3-1 at Goodison Park to finish in fifth position, but Neville has already turned his attention to next season, when he hopes the club can break into the top four.

Moyes will meet Bill Kenwright, the chairman, this week, when the manager will discover the size of his transfer budget before deciding whether to commit his long-term future to the club, and Neville is hopeful that the Scot will get the assurances he wants.

“We've had two good seasons on the run now and we're showing improvement every year,” Neville said. “Sixth last year and then fifth this season - the next step is fourth and I think there is miles more to come from this team. It is a very important summer for the club. We have to press on and, in footballing terms, it would be a major disaster if we didn't push on and keep progressing as a club. We have to bring in the right players, better players than we have already. We need the players who will get us into the top four.”

Moyes has identified Steve Sidwell, the 25-year-old Chelsea midfield player who would cost about £3million, and Michael Bradley, 20, the £4.5million-rated Heerenveen and United States midfield player, as potential targets, but Neville believes that the club must also try to compete for the players who are normally the preserve of Manchester United, Chelsea, Arsenal and Liverpool or risk standing still.

“We just need that little bit extra now,” Neville said. “In the big games, especially against the top four, maybe we have missed that special player a little bit, and that's what we need to find this summer.

“Now we have to be competing for players with the clubs above us. To catch them, we have to be looking at the same players they are. If not, fifth will be the maximum we can expect, but at the moment we look the likeliest to break into the top four.”