The Toffees have claimed 19 points from their first nine games of the season, leaving them sixth in the Premier League table ahead of this afternoon's matches.
The manager told Sky Sports News: "In any season you want to be in a strong position in the final third of the season. We have been very pleased with the start of the season and the way the squad is shaping up, now it is a matter of getting through the middle third of the campaign and seeing where that takes us.
"It is in our DNA to win trophies and leagues, and we need to use that to our advantage. You always work towards that. How long is it going to take? It could be a season, but remember that there is a huge difference between us and the group of teams working at a certain financial level.
"I always believe in football it is not always about finances. You just need the time to bridge that gap you have. We are not financially fighting with the clubs who are spending to win the league or get into the Champions League but I believe with the characters we have at the club we can challenge that but it will take time to bridge the gap."
Everton host Tottenham Hotspur tomorrow.