Home supporters broke through a fence and attacked the West Ham contingent seated in a reserved section behind their own team’s dugout at the AZ Stadium.
A brawl ensued in which West Ham players, including captain Declan Rice, attempted to intervene, with several running to the aid of relatives.
Police and stewards were quickly on the scene to prevent further confrontation and calm was restored after 10 minutes.
"While everyone hoped for a historic European match, it turned into a pitch black evening due to the events occurring at the referee's final whistle," AZ said in a statement on Friday.
"It turned into a night to reflect on with shame. Not because of the football game played, but because of the behaviour of some visitors. Unfortunately, we cannot use the word 'supporters' for these people.
"What happened is beyond all bounds. The club again sincerely apologises to West Ham United and the thousands of well minded AZ supporters who have also been inconvenienced by the misconduct."
The club said that together with the police, Public Prosecution Service, and Alkmaar’s municipality they would review footage to evaluate "exactly what happened, how it could have happened and what needs to be improved".
AZ added that appropriate consequences would follow for those responsible.
Dutch police on Friday told the ANP news agency they had not yet made any arrests but will review images to see if there was any criminal liability that might warrant an arrest.
There were also incidents outside the stadium, including around Alkmaar's train station, police said.
“It's annoying, it doesn't belong in our stadium. Preferably in no stadium,” said coach Pascal Jansen, whose side lost 1-0 on Thursday as West Ham completed a 3-1 aggregate triumph to reach the final against Fiorentina in Prague on June 7.
“I feel shame. You have to control your emotions, even on a night with a defeat."
Defender Pantelis Hatzidiakos was among several AZ players who spoke out against 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,” he 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.”
Police and stewards were quickly on the scene to prevent further confrontation and calm was restored after 10 minutes.
There was a similar incident in London last week when AZ supporters, including the family of coach Jansen, were accosted by West Ham fans after they celebrated the goal scored by the Dutch club in the first half of the first leg.
West Ham manager David Moyes said the incident had overshadowed the Premier League club's achievement.
"There was nothing we could do, or that West Ham as a club could do. Like anyone, if you saw your family members in trouble then you'd go and help out and that was the situation," Moyes told reporters on Friday.
"Unfortunately it's taken up a lot of the news and time. But we're not letting it take away from the fact we reached the final, which is a brilliant achievement."
There was a similar incident in London last week when AZ supporters, including the family of coach Jansen, were accosted by West Ham fans after they celebrated the goal scored by the Dutch club in the first half of the first leg.
