The FA alleges Mourinho's language was "insulting and/or abusive and/or improper".
While leaving the pitch, Mourinho wagged his little finger at the camera and at the same time said some words which translated in English, appeared to be "f*** off sons of b*****s".
The United boss has until 6pm on Friday to respond to the charge but he could be banned from the touchline when he faces old club Chelsea on Saturday.
The match was played in a tense atmosphere, United having denied a report earlier in the day that Mourinho would be sacked that weekend regardless of the result.
Mourinho will head to his former stomping ground once the worldwide break is over, with a trip to Stamford Bridge to face Chelsea when the Premier League campaign resumes.
United recovered from 2-0 down to complete a dramatic comeback with a 90th-minute goal from Alexis Sanchez.
Footage shows Mourinho saying something, apparently in Portuguese, while at one point looking into a camera, as he headed towards the tunnel after the final whistle.