David Moyes is ready to challenge the Premier League big boys after his Everton side continued their impressive start with a 3-0 win at Swansea City.
Everton sit second having picked up 10 points from their opening five games.
The Toffees fans were even singing 'We are going to win the league' by the end of the game and Moyes is pleased that they have something to shout about.
"It was great to hear the fans singing that as we have not heard it often at Everton," said Moyes.
"If we had won against Newcastle as we should have done, we would really be mixing it with the big boys.
"We have finished a lot of seasons strongly and the one year we got a good start, we qualified for the Champions League so we have to do it again if we can."
Moyes had extra praise for Anichebe, who found the net for the second time in two games.
He added: "He did well in midweek against Newcastle as well, with his goal and the one which he should have got [which was ruled out].
"He does not possess an awful lot of self-confidence but if he gets that and a bit of belief, he is a handful for defenders."
Everton face Leeds in the League Cup on Tuesday before welcoming Southampton to Goodison Park next weekend.