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.
European football’s governing body Uefa will review reports of the incidents before deciding on any action.
Bruce-Ball, who was commentating for BBC Radio 5 Live from the AFAS Stadion in the Netherlands, added: “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 stadium in Alkmaar, in the north of the country.
“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 said: “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.”
Midfielder Pablo Fornals added: “I was really concerned about how the family of my team-mates and the West Ham family are. Hopefully everyone is OK and the police can do their job and realise who did it.
“It’s not great when you are in that beautiful moment and people who aren’t try to use violence against you.”
Uefa has the power to appoint an inspector to investigate what happened if it is deemed to be serious enough.
AZ have yet to make any official comment over the incident but seem certain to be sanctioned.
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.”
Pantelis Hatzidiakos was among several AZ players who condemned the violence in post-match interviews.
“I think it’s sad what happened. My family was up there. I have been in contact with them and my girlfriend said they were shaking,” the Greece defender told Dutch television.
“I don’t even call them supporters. Just stay home if you have such intentions.
“Such a beautiful evening, such a great atmosphere, I really enjoyed it until the final whistle. What happened after that, I find very sad and a pity.”
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.”
‘Sense of nervousness’ over final security
Analysis by Simon Stone, BBC Sport
West Ham’s elation at reaching their first major final in 43 years is tempered by the knowledge that the venue in Prague which will host the match will not be big enough to hold the number of people who want to see it.
Their opponents, Fiorentina, are a similar club in the sense they have a big following and little recent success, in their case the Coppa Italia in 2001.
Uefa believe the game will be shown in fan parks, which may help. However, with a 20,000 capacity and a 5,000 allocation for each club, there is a sense of nervousness about how this will be managed and whether the security around the game will be up to the job.