The Belgium international still believes that his side can qualify for the Champions League this season, but insists that they must beat the likes of Reading if they are to do so
The Toffees have enjoyed a fantastic start to the campaign, and currently sitting fifth after losing just two of their opening twelve matches.
And with many finding it difficult to predict who will finish fourth this season, the Belgium international feels that David Moyes’ men have the ability to see off their competitors.
"Everybody in the team wants to finish in the top four," Fellaini told reporters.
"There is a lot of quality in the team, and a lot of ambition, and I hope at the end of the season, Everton will finish in the top four."
However, the 24-year-old conceded that the Toffees will have to secure points from sides such as Reading - against whom they lost 2-1 on Saturday.
"If you want to be in the top four, we need to win some difficult games, like Reading for example. It is difficult, but the team has the quality for this,” he continued.
"The manager was a little bit angry on Saturday because we had a lot of chances to win the game. We could have had two penalties, but that's football and it was disappointing for Everton.
"We need to win games like that if we want to finish in the top four. We will start again on Saturday. Getting three points is the most important thing."