The Scot was in defiant mood following the quarter-final defeat and was keen to stress that, although the Reds have only five league fixtures remaining with only a slim chance of a top-four place, the players have much to motivate them.
"Players have got to play well to stay in the manager's thoughts for next season - it's as simple as that," Fletcher told MUTV. "There's talk of a lot of changes and who knows? If you get an opportunity to play you've got to go out there and perform, and show the manager that you want to be at United.
"A lot of people will say there's nothing to play for in terms of league position or winning anything but there's a lot to play for in terms of personal pride and to be in the squad next season."
Fletcher's views were echoed by his fellow midfielder Michael Carrick who implored his team-mates to live up to the responsibility of playing for Manchester United and finish the season with pride.
"We've got a job to do [between now and the end of the season], we've got games to play and have a responsibility for this club and pride in ourselves.
"There are standards that we want to get to and there’s still an awful lot to play for. We want to finish strong and carry it into next season."