The Red Devils have drifted to 4-1 third favourites with most bookmakers after taking just four points from their opening three games.
United have also been criticised for their lack of activity during the summer transfer window.
However, Fellaini, who moved to Old Trafford in a £27.5m deal on deadline day, is convinced that there is enough quality within the current squad to challenge on all fronts this season.
"Of course we still have the quality to win the league," Fellaini told reporters. "I watched the game [against Liverpool] and in the second half, the team played well, played very well and had a lot of chances.
"My ambition this season is to win something with Manchester United and to play a lot of games for Manchester United. Winning a trophy is important.
"Of course it will be tough, we know it will be tough. But I think Manchester United has a great team and a great chance to win trophies so that is what I am looking forward to."