But he concedes that they will have to avoid results such as Saturday's 2-1 defeat at previously-winless Reading if they are to contend for a UEFA Champions League place.
The Toffees also failed to secure maximum points against the likes of struggling Wigan and QPR, but Fellaini insists the ambition of the players remains unaffected.
"Everybody in the team wants to finish in the top four," said the Belgium international.
"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.
"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.
"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."
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