Marco Silva was sent off during the game amid a 72nd-minute incident that resulted in United being awarded a penalty by referee Chris Kavanagh.
The Football Association alleges Silva’s post-match comments “constitute improper conduct in that they imply bias and/or question the integrity of the match official, and/or bring the game into disrepute”.
Silva, 45, has until Wednesday, 29 March to provide a response.
The charge is in addition to the Fulham boss having already been charged with abusive behaviour towards match officials during the 3-1 quarter-final defeat at Old Trafford.
Marco Silva is also facing an improper conduct charge for allegedly throwing a water bottle in the direction of the assistant referee.
United were awarded a penalty following a Video Assistant Referee (VAR) check that resulted in Brazil winger Willian being sent off for a deliberate handball on the line.
Kavanagh also sent Marco Silva to the stands for his actions on the touchline as the referee walked past him to view the pitchside monitor.
Fulham striker Aleksandar Mitrovic received a straight red card for pushing Kavanagh and is facing a lengthy ban.
“Our story with Chris Kavanagh this season has been tough for us,” said Marco Silva after the game.
“Unfortunately, we have been very unlucky with him this season. Many moments. It is difficult to understand some of the decisions.
“We had that West Ham game away from home [in October]. We lost the game with two clear handball goals and it was Chris Kavanagh in that moment. Today, everyone saw what is happening in this game. It is difficult for them to not look for these things.”