While they were handed one penalty, converted by Bruno Fernandes, United were furious after a second was denied involving Amad Diallo.
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United will now contact refereeing body PGMOL today, with United chiefs furious.
Amad appeared to be pulled to the ground in the Cherries penalty area moments before Ryan Christie equalised for Bournemouth.
Referee Stuart Attwell waved away United's appeals and the call was not overturned by VAR.
A James Hill own goal put United back ahead but, to rub salt into the wound, Bournemouth were then awarded a penalty for a push by Harry Maguire, who was sent off, with the game ending 2-2.
