The Premier League champions lost three matches in a row to start 2014, and although they recovered with a 2-0 win over Swansea City on Saturday, David Moyes' side still lie seventh in the table.
Moyes has struggled to replicate the feats of former United boss Sir Alex Ferguson, and rumours of rifts within the current squad continue to persist.
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"It gets us angry because we know it is not true," Fletcher said.
"We are there every day. The players are fully behind the manager. And Alex Ferguson being in the stand [watching games] has no bearing on anything. It is great to see him there supporting the team. It would be a worry if he wasn't.
"We have got to believe in ourselves and keep a close-knit group, making sure that the experienced players are guiding the younger players in the right way. Winning games helps that."
The 29-year-old has been left disappointed by the criticism that Moyes has received this season since taking over in the United dug-out, and he has urged the squad to use the sceptics as motivation in the second half of the campaign.
"It is as if some people have been waiting for it to happen and are really relishing it," he added.
"We've got to use that as fuel to prove them wrong. We've got some great, talented young players in this squad. We have to keep reiterating to them that they believe in themselves.
"They will come through it without a shadow of a doubt and will be better and stronger for it.
"Hopefully they will be the ones passing on advice to the next generation when I am long gone."