Moyes's side are unbeaten in seven league games after the 2-0 victory against Manchester City, thanks to goals from Steven Pienaar and Louis Saha.

Everton have bounced back after losing 6-1 at home to Arsenal on the opening day and Moyes insists there is more to come from a team that outplayed the Champions League contenders.

He said: "We have always been capable of going on a run. That's why I was grumpy in the early part of the season. We were not playing well.

"We had too many injuries and still have. We don't have all our players available but we are beginning to get a wee bit closer.

"Given the players we have at the club we are a match for most sides in the Premier League. We should be contesting high up the table.

"I know that if we put this level of performance in every week we will get the results we deserve because they are talented footballers."

No-one looked more talented than midfielder Marouane Fellaini, who showed his rising confidence by spinning away from City striker Craig Bellamy.

That outrageous piece of skill prompted a thunderous ovation from the fans and Moyes joined in the applause.

Moyes said: "He played really well and I have been saying for a while how good he is.

"He came into the Premier League at 21. He has got much stronger and much quicker around the field. Because of that he has grown into his role.

"He was only a young boy when he came. But even as a young boy he contributed nine goals to the team last year. He is doing well."

Pienaar made the breakthrough in the 36th minute with a 20-yard free-kick that evaded Shay Given at the goalkeeper's near post.

The goal was coming after a lengthy spell of Everton pressure and Saha extended their lead in first half stoppage time from the penalty spot.

He scored his 13th goal of the season after Micah Richards had tugged his shirt inside and outside the box.

Everton came close to extending their lead with both Fellaini and Tim Cahill seeing efforts come back off the woodwork.

It was City's first defeat in five games in all competitions under manager Robert Mancini and he had little complaint, apart from stating the penalty should not have been awarded.

He realises there is much work to do and the result will hardly boost confidence ahead of the Carling Cup semi-final first leg against Manchester United on Tuesday.

Striker Roque Santa Cruz looks likely to miss the derby after suffering a calf problem at Goodison Park and Mancini said: "We have a number of injuries and that is a worry for us."

Expectations are high at City but the former Italian boss added a note of realism after suffering his first defeat.

"I am not a magician. I am a manager and I do not think I can change the situation in a month, " said Mancini.

"But I believe we can improve game after game. That is possible. "It is a long season."