Supporters were gathered outside the east London stadium, which has been West Ham's home since 1904, before the last home game ahead of next season's switch to the Olympic Stadium.
Manchester United's team coach was stuck outside the car park, and captain Wayne Rooney blamed home fans for attacking it.
"The coach got smashed up but we'll just have to go and prepare and get on with our job," the England star told UK match broadcaster Sky Sports before his team's 3-2 defeat.
However, West Ham co-chairman David Sullivan blamed Manchester United for not turning up earlier.
"Man United should have got here at 4 p.m.," he told Sky Sports. "They know it's our last game. They had the same problem at Tottenham a few weeks ago. I think the police and officials have been kind. I'd make them kick off at 7.45 p.m. if I was in charge."
"I'm gravely disappointed, more for our supporters. What people forget is they've got trains and buses to get home and we've got a wonderful, wonderful show after the game for them. Many just can't stay any more."
Manchester United's match at Tottenham in north London last month was delayed by 30 minutes because the visiting team's bus was stuck in traffic.
The club's manager Louis van Gaal said Tuesday's incident was "not so nice."
"The way we have been received is not the proper way," the Dutchman told Sky Sports before the game kicked off.
The UK Press Association said police had made no arrests, and Scotland Yard confirmed an officer and a member of the public had suffered "minor injuries."
"We are aware that a number of items were thrown towards Manchester United's coach this evening," the police said in a statement, PA reported. "An appropriate policing plan is in place."
Pictures from the Getty Images agency showed damage to the bus' external window glazing, while videos were posted on social media showed bottles being thrown at the vehicle.
Tuesday's result was a big blow to Manchester United's hopes of finishing in the top four and claiming a place in next season's European Champions League qualifiers.
Fourth-placed rival Manchester City has a two-point advantage ahead of this weekend's final round of Premier League matches.
City travels to Swansea on Sunday, while United will host Bournemouth.
West Ham, which visits Stoke, is three points behind City in sixth place as the club seeks to qualify for the second-tier Europa League.
Diafra Sakho put the Hammers ahead in the 10th minute on Tuesday from Manuel Lanzini's cutback.
However, Anthony Martial equalized soon after halftime from Juan Mata's assist, and the 20-year-old France forward put the visiting team ahead in the 72nd minute from a counter attack started by Rooney.
West Ham hit back almost immediately as Michail Antonio headed in from Dimitri Payet's delightfully flighted past. Five minutes later, the French playmaker supplied the free-kick which New Zealand center-back Winston Reid nodded into the net despite keeper David de Gea getting a solid hand on the ball.