The Red Devils conceded in the closing stages of the first period against the Bees, with Ethan Pinnock heading into the back of the net, but there as controversy surrounding the goal.
Matthijs de Ligt was forced to leave the field for a third time to address a cut on his head before the corner was taken, and the Netherlands international was then not allowed back on until after the set piece.
Man United head coach Erik ten Hag and assistant manager Ruud van Nistelrooy both picked up yellow cards after making their point to the officials, but Fletcher showed his fury in the tunnel, and the Scot has now been hit with a misconduct charge.
"Darren Fletcher has been charged with misconduct following Manchester United's fixture against Brentford on Saturday, 20 October, in the Premier League," read a statement from the Football Association.
Fletcher charged by FA after De Ligt incident
"It is alleged that the coach acted in an improper and/or confrontational manner and/or used abusive and/or insulting words towards the fourth official and the referee and/or assistant referees. Darren Fletcher has until Tuesday, 29 October, to respond."
Fletcher is believed to have made his feelings clear to referee Samuel Barrott and fourth official Gavin Ward as the officials made their way down the tunnel at the interval of the clash.
Man United did manage to turn the game around in the second half, recording a 2-1 victory courtesy of goals from Alejandro Garnacho and Rasmus Hojlund, with the result easing the pressure on head coach Ten Hag.
Fletcher was appointed Man United's technical director in 2021, but he switched to the role of first-team coach over the summer after the arrival of Jason Wilcox at Old Trafford, with new minority shareholder Sir Jim Ratcliffe making sweeping changes.
When are Man United next in action?
Man United were in Turkey on Thursday evening for a Europa League clash against Fenerbahce, with the match finishing 1-1, and the Red Devils will now switch their attention back to the Premier League.
The 20-time English champions will head to the London Stadium on Sunday afternoon to tackle West Ham United, before welcoming Leicester City to Old Trafford next Wednesday in the EFL Cup.
Man United are currently 12th in the Premier League table, six points behind fourth-placed Aston Villa.