West Ham United will ban for life anyone found to have thrown missiles at the Manchester United team bus.
The FA will also investigate incidents before and during the Hammers' final game at the Boleyn Ground on Tuesday night.
United's team bus was attacked as it tried to make its way into the ground, with windows damaged after objects were thrown at it.
Footage apparently taken by United player Jesse Lingard showed the players taking refuge in the aisle down the centre of the bus as bottles and cans smashed against the windows.
Items were also thrown inside the stadium and the FA will look at the matter in closer detail.
On the way to the ground Sky Sports News HQ understands that the United bus was just a couple of hundred metres behind the West Ham team coach.
But around half a kilometre from the stadium the United bus was held up for around 50 minutes by the crowds.
SSNHQ also understands United received no warning about the congestion - and therefore the potential for delays - and when it became clear they would not make it to the ground on time, it was United who contacted the league.
West Ham's co-chairman David Sullivan, speaking before the extent of the trouble became apparent on Tuesday evening, initially complained that United should have allowed more time to get to the ground, and suggested the behaviour was no more than "over-exuberant".
But on Wednesday he said: "If we were to have scripted how our final game at the Boleyn would have played out, it wouldn't have been much different to last night's match.
The West Ham family then all celebrated our legends and former players together in what was a truly fitting ceremony to say goodbye to our home of 112 years.
"Sadly, the actions of very small minority of people outside the ground prior to kick-off risks overshadowing those celebrations. I want to be clear - their behaviour was completely unacceptable and does not represent our club or our values.
"When I was asked about the incident prior to yesterday's game, I was unaware of the damage that had occurred to the Manchester United team bus. I want to apologise to Manchester United for that damage and assure them that we will be doing all we can to track down those responsible and ban them for life.
"This morning I have already tasked my senior team to work with the police to identify them as their behaviour belongs in the past and not in a future that promises so much for our great club.
"I truly hope that in due course we will look back on what happened in the stadium rather than what happened outside and remember our farewell to the Boleyn for all the right reasons."
A statement from the FA was released after the match, which ended 3-2 to the Hammers after Winston Reid headed home 10 minutes from time.
It read: "The FA strongly condemns the unsavoury incidents this evening involving both the Manchester United team coach outside West Ham United's Boleyn Ground and objects thrown from a section of the home support during the game.
"We will work closely with both clubs and the Metropolitan Police to fully investigate these matters."
The Metropolitan Police confirmed on Wednesday morning that four officers suffered injuries during the trouble outside the ground.
"No arrests have been made so far in connection with the criminal damage caused to the coach. Inquiries are ongoing," the force confirmed.
"Three men were arrested during the course of the match: A 20-year-old man arrested on suspicion of affray; a 47-year-old man and an 18-year-old man were arrested for pitch incursion. They have all been taken to an East London police station for questioning."
The Met would not reveal how many officers they had on duty.
They told Sky Sports News HQ that matches are policed on a grading system, but would not confirm what grade the match was.
The Met would only say that an "appropriate policing plan was in place" and that "the incident is being fully investigated".
The kick-off to the match was delayed by 45 minutes because of United's difficulties getting to the ground.
On Wednesday morning West Ham vice-chairman Karren Brady used Twitter to condemn the attack on United's bus.
"I, the Board and everyone at West Ham United totally condemn the unacceptable behaviour we saw outside the ground last night," Brady wrote.
"West Ham is a family club and the vast majority of fans attended Tuesday's Final Game to respectfully say Farewell Boleyn.
"Those who chose to behave unacceptably will be dealt with in the strongest way possible, with life bans for those guilty of violence.
"The events in the stadium last night were incredible and it would be a shame if the actions of a mindless few outside overshadowed them.
"Their behaviour was unacceptable and won't be stood for. But my overriding memory will not be of them but of a fitting farewell to the Boleyn."
Manchester United skipper Wayne Rooney spoke to Sky Sports after the coach finally reached the ground.
"It wasn't nice. The coach got smashed up, but we are here now," Rooney said. "I'm sure you'll see the images. It's not for me to say, but it was disappointing of course.
"It's a big night for West Ham, but I'm sure West Ham as a club will be disappointed with what the fans have done."
West Ham boss Slaven Bilic intimated after the game that it was a lack of policing which had led to the incident.
"That is not a question for me," he replied when asked about the pre-match trouble.
"It was strange for me, I don't want to teach lessons to the people in Canary Wharf. In Canary Wharf if you poke your nose you have two policemen surround you saying you can't do that.
"Here you have a football game, 50,000 people on the street, that is kind of strange to me."