The North-West outfit were knocked out of the tournament at the quarter-final stage by Bayern Munich on Wednesday night.
The club are also expected to miss out next season due to the Red Devils currently being seven points behind fourth-placed Arsenal in the Premier League with five games to play.
"This is the pinnacle of club football," BBC Sport quotes Fletcher as saying. "Manchester United need to be in this competition. We won't be there next season and that is disappointing.
"Next season is a big season. We are not just thinking about getting into the Champions League. We will think about winning the league and getting into the Champions League off the back of that.
"Players have to play well to stay in the manager's thoughts for next season, it is as simple as that. There is talk of a lot of changes. If you get an opportunity you have to go out there and perform, show the manager you want to be at United and that you are good enough to be at United."
United currently reside 17 points adrift of league leaders Liverpool.