England had three centurions on the pitch in Kiev, but against Moldova at Wembley in the previous match there were three Evertonians. When Ross Barkley trotted on to join Phil Jagielka and Leighton Baines for the last half an hour Everton had three players in Three Lions shirts for the first time since Trevor Steven, Gary Stevens and Dave Watson played against Russia 25 years ago.

Go back a little further and you could find four Everton players in the England team for the 1986 World Cup in Mexico, with Gary Lineker and Peter Reid joining Steven and Stevens to line up against Argentina for the "hand of God" game. In those days, of course, Everton under Howard Kendall were winning titles at home, and while no one is suggesting that Roberto Martínez is now well placed to do the same thing, it is clear that the Goodison legacy left by David Moyes is a healthy one.

Particularly as Martínez is already starting to promote another promising English player in John Stones, a 19-year-old centre-half Moyes signed for £3m from Barnsley in January. Wigan actually offered Barnsley the same amount for Stones in the winter window and thought they were close to a deal, only for the then Under-19 international to plump for higher-flying Everton. He did not actually get a game under Moyes last season, whereas he could have ended up with an FA Cup winners medal under Martínez, but he was not to know that at the time.

The former Wigan manager is delighted to have the defender in his control at last, and though Jagielka and Sylvain Distin remain the first-choice centre-back pairing at the moment, with Antonín Alcaraz also in contention, everyone could see from the confidence Stones displayed in the pre-season friendlies that Everton have a player for the not-too-distant future. "I think he is the most promising English centre-half around," Martínez said. "It was frustrating to miss out on him in January because I thought then he was ready for the top flight. At Everton he will get a little more time to develop but he has a fantastic future ahead of him."

Everton were widely judged to have had a successful summer transfer window, or at least a successful conclusion to it, since they kept Baines and managed to extract £27.5m from Manchester United for Marouane Fellaini. The imposing Belgian was an important asset to Everton under Moyes, who now faces the task of proving he can be as useful at Old Trafford. Martínez had already moved Fellaini back to a defensive midfield position at Goodison, and the manager has ended up with Gareth Barry for that role, with James McCarthy alongside him. At post-Fellaini Everton not only Darron Gibson must be feeling his appearances may be limited, there could be some tough choices to make too affecting established players, with not even Leon Osman, Steven Pienaar and Kevin Mirallas immune from the new pressure on places.

Clearly not everyone is going to get a game if Barry, McCarthy, Barkley and Romelu Lukaku are going to be regulars, and there does not appear to be much doubt about that. McCarthy's fee alone dictates he will be a first-choice player – Everton are not the sort of club to pay £14m for a reserve. Barkley is proving good enough for England, people are already predicting a Wayne Rooney-type career trajectory, and if that turns out to be the case Everton need to get games out of him while they can. He is the sort of player who can influence outcomes and he is obviously ready. "I don't think Ross realises how good he is half the time," an admiring Jagielka said. "He's had so much expectation chucked on his shoulders but he just takes it all in his stride."

That only leaves Barry (Lukaku will be a straight slot-in as a new front man once he becomes eligible to play, but despite all the Evertonian excitement he is going to have to sit out the next game against his parent club Chelsea). The Manchester City capture is also a loan signing, though his parent club is looking for a permanent sale, and Barry could end up staying for longer if this season goes well. He has not come to Goodison to swap one bench for another, and Martínez certainly seems to envisage Barry as his new midfield anchor. "Gareth's arrival will be instrumental to what we are trying to do," the Everton manager said. "There aren't too many English players who can fulfil the role he does, and because of his age and his vast experience he brings know-how. You always need that balance in a team, and young players such as Ross Barkley, James McCarthy and John Stones will all benefit."

Barry is 32 now and needs to be playing to keep his hopes of an England recall alive, though he denies he agreed to the move to resurrect his international prospects. "I just want to play, as soon as I knew Everton were interested I was keen for the move to go through," he said. "If I play well here I could get back into the England squad, who knows, but I would regard that as a bonus. This could be my last chance to play in a major championship, as it might be for a few of the other lads."

All Everton need now is a win, for which they will require a goal or two, since the past two of their three draws this season have been scoreless.

Martínez will hardly be pilloried if he fails to get the desired result against Chelsea, though he did manage to beat them in his time at Wigan, but he needs to pick up three points from at least one of the remaining fixtures this month – the other two are West Ham away and Newcastle at home – to avoid going into October still searching for a first victory. The first game in October is Manchester City away and it will be interesting to see whether Martínez can keep up Everton's generally impressive record against the Manchester moneybags. Confidence could be key and that can only stem from previous results.

At Wigan, at least until the roof fell in towards the end of last season, Martínez managed to keep the fans onside despite some shocking performances by virtue of some genuinely surprising victories over leading sides. Wigan more or less expected to be near the foot of the table though, whereas Everton set their sights on higher things. Averaging a point per game used to see the Latics right most seasons, give or take the inevitable narrow scrapes come April. Everton are looking for something more convincing. They have the players, they just need to post the results to announce the Martínez era has properly begun.