The Scottish midfielder believes that United, who are currently seventh in the Premier League, can bounce back to become one of the top teams once again. He also claims that they should not be written off in the Champions League ahead of their quarter-final tie with Bayern Munich.
"There's always been difficult times and it's a test of character I think," Fletcher told Sky Sports News. "You've got to look around the dressing room and I see good characters.
"We've all got to dig together, the staff, the players, everyone. It's a time for big characters, and big characters come through it. That remains to be seen whether we can, but I believe we can. I know we can.
"We're still in the Champions League and people write us off - we're playing Bayern Munich - but what a challenge that is. You're playing Bayern Munich in a Champions League quarter-final."
Moyes's side host Bayern in the first leg of their last-eight tie on Tuesday.