West Ham players confronted a group of AZ Alkmaar fans who attacked an area in which their friends and family were watching the teams' Europa Conference League semi-final second leg.
Michail Antonio and Said Benrahma were among those who tried to intervene in the clashes moments after the Premier League team had reached the final.
BBC commentator Alistair Bruce-Ball, who was inside the stadium, said he saw punches being thrown by the AZ fans.
"These are awful scenes," he said.
"Some fans clad in dark coats and hoods up came racing down in front of the lower tier of the stand to voice their dissatisfaction, and there is trouble to our right-hand side.
"The concern here is I think the West Ham family members and friends are in that section. Those are very, very unpleasant scenes.
"The West Ham players are being held back. I can see in the distance punches being thrown."
'We were worried about them'
West Ham manager David Moyes, whose 87-year-old father was reportedly among the crowd, said his players were angered by what had happened in the AFAS Stadion.
"We'll need to wait for the dust to settle to see what it is but the biggest problem is that is the area where the players have all their families in," he said.
"That is where the problem came, and a lot of players were getting angry because they couldn't get to see if they were OK.
"What I don't want to do in any way is blight our night. It wasn't West Ham supporters looking for trouble.
"Was I worried? Yeah, my family were there and I had friends in that section. You're hoping they would try to get themselves away from it.
"Security wanted to take me inside, but I had to make sure my players weren't involved."
Hammers goalkeeper Alphonse Areola added: "When families or friends are coming to the stadium, we don't want to see things like that. They want to enjoy the event and we want to enjoy it with them as well. We were worried about them."
West Ham reached their first major European final since 1976 by beating their Dutch opponents 1-0 on the night and 3-1 on aggregate.
During last week's first leg at London Stadium, family members of AZ players had been involved in a confrontation with West Ham fans.
AZ boss Pascal Jansen said: "What happened last week was very unfortunate and then you get the same feeling as what happened tonight.
"I feel a little bit ashamed it happened in our stadium but you have to control your emotions."
Former Hammers midfielder Joe Cole, who was part of the BT Sport team covering the match, said what happened was "absurd".
"Grown men attacking the West Ham fans," he said. "Players were trying to get involved to break it up.
"AZ Alkmaar fans turning up wearing balaclavas throwing punches is ridiculous."
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