United, who saw their hold on the trophy ended with a 1-0 defeat by the Premier League leaders, were punished for several of their players surrounding referee Michael Oliver and arguing with him over the sending off of Spanish midfielder Ander Herrera in the 35th minute.
Herrera was given his marching orders for a foul on Eden Hazard seconds after Oliver warned United captain Chris Smalling his patience had worn thin with continual fouls on Chelsea's Belgian playmaker.
"Manchester United have been fined £20,000 after the club admitted an FA misconduct charge and accepted the standard penalty," said an FA statement on Friday.
Herrera and United's leading scorer Zlatan Ibrahimovic will miss the Premier League matches with struggling Middlesbrough on Sunday and against West Brom on April 1 because of suspension.
Ibrahimovic was banned after elbowing Bournemouth defender Tyrone Mings in the head in a 1-1 league draw at Old Trafford.