How Joe Hart may fare in England's final two World Cup qualifiers remains a live issue after this game. From his seat in the directors' box, Roy Hodgson told friends he was happy with Hart's display as the England manager prepares for Friday's meeting with Montenegro and next week's match against Poland, both at Wembley. Yet when called upon to save Romelu Lukaku's 16th-minute shot, Hart was unable to do so despite the ball being close enough for the goalkeeper to comfortably get a hand on it.

That made it 1-0 to Everton and though Hart did little else wrong, Hodgson may wonder how Hart will perform should Montenegro prove a greater goal threat than Roberto Martínez's side.

At the close Hart's relief was obvious in the way he hugged Xabier Mancisidor, the Manchester City goalkeeping coach, near the technical area: it was a lingering head-into-shoulder embrace that illustrated where Hart is mentally.

Pablo Zabaleta said: "Most of the lads saw him a bit down in the week but we need him to come back again to his best. Sometimes it happens in football, that's why it is important that, as team-mates, we need to support all the players. And he knows all the players are behind him.

"We've seen him for a long time doing very well and that is why it is strange to see him down. As players sometimes we are not in a good moment but it is important to respond well and try to come back to your best."

Of the Lukaku goal, the right-back said: "He's still upset about it. He felt he could have got a stronger hand to it. Sometimes it is really hard for any player when you are not doing well. It is important for him to show his strength of character; he has to show his strong personality and show he is coming back to his best. I'm sure he will do that because he is a great goalkeeper."

The hope is that Hart can recover the old swagger and consistency that has him correctly billed as head and shoulders above the rest of English keepers.

There was goodwill from Martínez for Hart. "Goalkeeper go to both extremes, they are heroes but also the last line. You need to understand there will be ups and downs," he said.

The negative for Everton was that this defeat ripped up the division's only unbeaten record. In the opening half their better performers were Ross Barkley, Kevin Mirallas and Lukaku but these three, along with the rest of their team-mates, faded after the interval.

Still, there was enough evidence to suggest Everton could reach the turn of the year challenging for a Champions League berth. Martínez said: "We are still very early in the season, it would be foolish for us to be saying that now. We need to use the first two-thirds of the season to see how many points we can get."

Barkley's ability to ease past a defender while seeing a killer pass is reminiscent of a youthful Paul Gascoigne, and the manager said: "He has such a terrific talent but he's still developing into a player. He's showing signs of someone who can be very special because he controls the ball with both feet.

"He can turn both ways, great balance, he is something special. But we will see him develop and become himself – I don't think we can compare him to anyone. He can play in different positions."

Barkley, at 19, is in Hodgson's squad this week. "I always said I am happy with Ross going with England, it's a terrific experience," said Martínez. "He's such an exciting character who is going to be representing his country. Roy knows Ross really well from the under-21s.

"He's someone that is still growing and developing – but I'm not concerned about him being involved. Ross is not going to be someone who has all the pressure on him. He brings something different and he can be used. It's very different to other members of the squad.

"Nothing fazes him, you look at the time he was out with injury, fighting to get in the first team, out on loan. You can imagine the challenges he's faced. Now he's representing England and being an important player for Everton."

Tim Howard was the unfortunate sufferer of an own goal when Sergio Agüero's 68th-minute penalty was palmed by the keeper on to his left post only for the ball to rebound back off him and in.

Before that Howard had been at fault, in similar fashion to Hart, when allowing Alvaro Negredo's 17th-minute shot to slip by him. The Spaniard's fourth of his debut City season was the equaliser, and his side entered the break in the lead after Agüero sprinted down the right before unloading a finish that gave Howard no chance.

Man of the match Alvaro Negredo (Manchester City)