West Ham players were confronted by a group of AZ Alkmaar fans who invaded the area where friends and family were watching the Europa Conference League second leg.
Michail Antonio and Said Benrahma were among those who tried to intervene shortly after the Premier League side reached the final.
BBC commentator Alistair Bruce-Ball, who was inside the stadium, said he saw punches being thrown by AZ fans.
“This is a terrible situation,” he said.
During last week’s first leg at the London Stadium, relatives of AZ players were involved in an altercation with West Ham fans.
Hammers manager David Moyes says his players are angry about what happened at AFAS Stadion.
“We have to wait for the dust to settle to see what it is, but the biggest problem is that the place where the players have all their families,” he said.
“This is where the problem came, and many players got angry because they couldn’t see if they were okay.
“Let’s wait and ask the officials what really happened. I can only tell you that the players were affected because they are part of their family.”
West Ham reached their first European final since 1976 by beating their Dutch rivals 1-0 on the night and 3-1 on aggregate.
Moyes, who said his family and friends were in the area that was attacked, added: “What I don’t want to do in any way is spoil our night. It wasn’t West Ham fans looking for trouble.
“Was I worried? Yeah, my family was there and I had friends in that area. You hope they try to get it out.
“The defense wanted to take me in, but I had to make sure my players weren’t involved.”
AZ boss Pascal Jansen said: “What happened last week was very sad and you feel the same way about what happened tonight.
“I’m a little embarrassed that it happened in our stadium but you have to get your emotions under control.”
Former Hammers player Joe Cole, who was part of BT Sport’s coverage of the game, said the incident was “absurd”.
“Big men are attacking West Ham fans,” he said. “The players tried to get involved to destroy it.
“AZ Alkmaar fans turning up wearing balaclavas to throw punches is ridiculous. There were families.”
‘I see punches being thrown’
Bruce-Ball, who is a commentator on BBC Radio 5 Live in the AFAS Stadion, described the incident as “unpleasant”.
“Some fans wearing black shirts and tops climbed in front of the lower part of the stand to express their dissatisfaction, and there is a problem on our right,” he told the audience.
“The concern here is that I think the family and friends of West Ham are in the area. This is a very sad situation.
“West Ham players are being pushed back. I can see punches being thrown in the distance.”