Moyes is relishing the task of challenging for the top four.
Asked whether he was excited about this season he said: "Quite but not madly.
"We've only played 11 games and there are a lot of good teams below us - Tottenham, Liverpool, Arsenal, Newcastle - who could quite easily jump over us and West Brom are having a great season as well.
"I am not going to say we have no chance because we have got a chance but the competition is really tough.
"For Everton it is very rare for us to say we are having a good start.
"If we can have a second half to the season what we've had in recent years tagged on to this then it could be an exciting season - but there are a lot of ifs."