The visitors were met by thousands of West Ham supporters as they attempted to make their way into Upton Park, and images and videos posted on social media showed windows having been broken after objects were thrown at the vehicle.
Prior to the game, Manchester United captain Wayne Rooney said that the coach had been "smashed up", and West Ham have released an official statement to condemn the incident that resulted in kickoff in East London being delayed by 45 minutes.
It read: "It was an extraordinary night full of extraordinary moments in front of extraordinary fans. 99% of whom behaved impeccably and were a credit to the club.
"We have already had thousands of tweets and emails from fans to say how proud they were to be a part of such a special evening in West Ham's history.
"However, we are aware that there were some supporters outside the Boleyn Ground who didn't act in an appropriate way when the Manchester United team bus was damaged.
"That was not acceptable and we will work with the police to identify those responsible and ban them for life."
The match ended in a 3-2 victory for West Ham, who netted twice in the final 14 minutes to end life at their long-term home in fairytale fashion.