Clattenburg sent off Chelsea pair Branislav Ivanovic and Fernando Torres in the second half at Stamford Bridge, and the Premier League leaders subsequently accused him of speaking out of turn to two of their players.
"We have lodged a complaint to the Premier League match delegate with regards to inappropriate language used by the referee and directed at two of our players in two separate incidents in today's match," said a Chelsea spokesperson.
"The match delegate will pass the complaint to the Football Association. We will make no further comment at this time."
It was reported by the Daily Telegraph on Monday that one of the complainants, believed to be Nigerian midfielder John Obi Mikel, claimed Clattenburg directed a comment of a racial nature at him.
A spokesperson for the Professional Game Match Officials' Board, the body which represents referees said it was "aware of the allegations and they are being treated with the utmost seriousness.
"Mark will cooperate fully and welcomes the opportunity for the facts to be established. No further comment will be made until this matter has been properly investigated," added the spokesperson.
Chelsea were also aggrieved that Clattenburg allowed United's 75th-minute winning goal to stand, despite Javier Hernandez having been in an offside position prior to scoring.
The defeat ended Chelsea's unbeaten start to the season and allowed both United and Manchester City to close to within a point of Roberto Di Matteo's side at the top of the table.
Chelsea have also launched an investigation into reports that a steward was injured by objects that were thrown onto the pitch in the aftermath of Hernandez's goal.
Chelsea fans in the Matthew Harding Stand hurled abuse and appeared to throw objects at the United players as they celebrated their winning goal.
The steward fell to the floor during the incident and needed approximately 10 minutes' treatment by paramedics before being taken to hospital.
"We are looking at reports of objects that may have been thrown or incidents around the steward taking a fall," a Chelsea spokesperson said.
"We are investigating all the incidents around that time. My information so far is that he slipped and fell, may have hurt his knee, and was being treated by the side of the pitch." – Sapa-AFP