The Premier League champions are currently seventh in the table but Fletcher is confident that an impressive finish to the campaign will help them claim one of the top four spots.
"It's all about character now, no doubt about it," Fletcher told Sky Sports News. "The team has been written off, everyone has had so much to say about the situation and it's now time for the players to step up and prove people wrong and to finish the season strongly.
"As I keep saying let's finish the season strongly, get in the Champions League - we're still in the Champions League this season as well and our form has been fantastic - and let's carry that through to next season."
United host Fulham at Old Trafford on Sunday afternoon.