A 3-1 loss to Bayern Munich in the Champions League on Wednesday night signalled David Moyes' last chance to win major honours this term, with the club already out of the running for all domestic prizes.
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"The boys have got to play well to stay in the manager's thoughts for next season," Fletcher told reporters.
"There is talk of a lot of changes so if you get an opportunity to play you have to go out there and perform and to show the manager that you want to be at United, that you are capable of being at United and you are good enough.
"A lot of people will say there isn't a lot to play for now, but there is - you are playing for personal pride and to be in the squad for next season."
With United bracing themselves for their first season without Champions League football since 1995, Fletcher feels the club should "embrace" the Europa League if they qualify come the end of the season.
"We should embrace it. Let's go and win it," the 30-year-old said. "Next year we won't just think about getting into the Champions League, we will think about winning the league and getting into Europe that way."
"The gap is not as big as people think. We have some fantastic players. There will be some signings too and hopefully they can take us to where we want to be."