David Moyes received another text from Tim Cahill last Saturday evening. "That was fantastic," was the verdict from New York on Everton's emphatic recovery against Southampton. Only a fool would have disagreed. Cahill joined Red Bulls in the summer but it is his former club who have been given wings.

Second in the table and more importantly at this stage, playing with a confidence and style not witnessed at Goodison Park for many a year, Everton's start has attracted admiration from the Australia international and beyond. "He's been in touch after games two or three times this season," says Moyes. "Apparently he thinks he's mayor of New York now. I'll probably take the team out to see him in New York if I get the chance." The longer-term incentive is a journey into Europe.

With 13 points from six league games, Everton have responded to criticism of their repeated poor starts and produced an identical points tally to 2004-05 when they reached the Champions League qualifiers. But it has been done in a more expansive, entertaining and adventurous fashion than when nine 1-0 wins helped them to fourth eight years ago. Moyes's team head for Wigan Athletic on Saturday with an average of 21 goalscoring chances per away game.

The Everton manager admits: "I think there is a difference in the quality but we had really good players then, good senior players, and if you said the quality is better now I'm sure they would rebut that. The challenge I am setting to the boys now is can you be as consistent as the team from 2004-05? That is part of the battle.

"You can win with flair but we won a lot of games 1-0 that year. We were consistent, hard to beat. There are different ways of skinning a cat. We are in good form just now but how long can we keep it going? It is a test of the players to keep reaching those standards."

In Cahill, Lee Carsley, Duncan Ferguson, Alan Stubbs and co, Everton were not short on character when they last competed at the top. Moyes sees no difference today. "Spirit exists here and it has grown," he says.

"Spirit is in the DNA of the club, it is in the building and I think it is around Goodison Park. A lot of that keeps Everton going. I think people walk into Everton and there is an energy, the sense of a working club and a good atmosphere. That is a good environment to work in."

The recovery from a fractured start to last season on and off the pitch began in January when the sale of Diniyar Bilyaletdinov helped fund the signings of Darron Gibson and Nikica Jelavic. Steven Pienaar, left, arrived on loan, then permanently in the summer from Tottenham Hotspur, and has been joined by Kevin Mirallas, Steven Naismith and Bryan Oviedo. Jack Rodwell apart, the squad remained intact this summer and there is arguably more depth and attacking options available to Moyes than at any time during his decade in charge.

"A little bit of money, a little bit of changing around and a bit of wheeling and dealing have made a big difference," he explains. "The squad was getting older so we brought younger players in and changed the age group." But, and as an early League Cup exit at Leeds illustrated, there is cause for caution amid the optimism and praise.

As Moyes, who has been named manager of the month for September, adds: "The balance of the team is good but the squad could still be a bit light. That, in the end, could catch me out. We are still short of central-midfield players and if you're talking about a squad to compete at the top end of the Premier League, I'm worried we are not going to have that level."

Moyes has appeared far more relaxed this season – though he is out of contract next summer and yet to sign an extension – and his team seem more ambitious. Yet after a summer when talk of a move to Tottenham proved only that, he denies there has been an overhaul in his managerial philosophy.

He states: "Folk think I'm defensive but I was brought up on the best attacking team ever in terms of style and what was demanded, Glasgow Celtic. I have also played under coaches who showed me another style. I want my team in the opponents' half having shots. I've only been brought up that way and no other way. But you can only win games with the tools you have available and if you don't have them you need to find other ways of winning. Otherwise I wouldn't still be in the job.

"I didn't have the tools to win that way five or six years ago. What I have had is time to get to the point where I am now being asked about being entertaining."