Pablo Fornals’ stoppage-time goal earned the Irons a 1-0 win on the night and a 3-1 aggregate victory which sees the club into their first major European final since 1976.
Uefa protocol means that travelling teams are given an allocation of corporate tickets within the home stand at matches, rather than in the main away end.
At the full-time whistle, having seen the West Ham entourage’s celebration of the late goal, a group of hardcore supporters from the ultra end of the ground raced around the edge of the playing field to attack the visiting supporters.
West Ham’s players raced to the situation, with many of their family members evidently caught up in the melee, while local police appeared slow to intervene.
Hammers boss David Moyes admitted afterwards that he had been concerned for his own family and friends and called for an investigation into the trouble, though hoped it would not overshadow a historic night for his team in Europe.
"I can only only say the players were involved because it was the family section and most of their family and friends were in there. That was probably the reason for the reaction,” he said.
"Was I worried? Yeah, my family were there and I had friends in that section. You're hoping they would try and get themselves away from it.
"I didn't recognise it because I'd gone onto the pitch. Security wanted to take me inside, but I had to make sure my players weren't involved.
"What we don't want to do is in any way blight the night because it certainly wasn't West Ham supporters looking for trouble. Hopefully they'll look into it."
Alkmaar’s London-born boss Pascal Jansen apologised for the trouble and said he was “ashamed” that it had happened.
“I feel ashamed it happened in our stadium. It should not be happening. You have to stay in control of your emotions.”