According to BBC Sports, West Ham will issue life bans to any fans found responsible for attacking the Manchester United team coach before Tuesday’s game at Upton Park.
A window on the bus was smashed and the kick-off delayed by 45 minutes as a result of the trouble.
“We are aware that there were some supporters outside the Boleyn Ground who didn’t act in an appropriate way,” a club statement read.
The Football Association also condemned the “unsavoury incidents”.
It added: “We will work closely with both clubs and the Metropolitan Police to fully investigate these matters.”
Bottles were also thrown at Manchester United goalkeeper David de Gea during the match, while another fan invaded the pitch to confront the Spaniard.
West Ham eventually won by 3-2 in what was their final game at the ground before moving to the Olympic Stadium.
The club statement continued: “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, said the behaviour of some fans was “not acceptable” and said it “will work with the police to identify those responsible and ban them for life”.