Pablo Fornals’ stoppage-time strike, which earned a 3-1 aggregate victory and sent them to next month’s final in Prague, prompted a gang of black-shirted, hooded AZ ultras to attempt to storm into the area reserved for friends and family behind the dugout.
Players including Michail Antonio, Said Benrahma, Aaron Cresswell and Flynn Downes climbed over the advertising hoardings in a bid to stop the trouble.
An AZ statement read: "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. It turned into a night to reflect on with shame.
"Not because of the football game played, but because of the behaviour of some attending. Unfortunately, we cannot use the word ‘supporters’ for these people.
"What happened is beyond all bounds. The club again sincerely apologises to West Ham and the thousands of well-minded AZ supporters who have also been inconvenienced by the misconduct.
"In the coming period AZ will - together with the police, Public Prosecution Service, and Alkmaar’s municipality - evaluate exactly what happened, how it could have happened and what needs to be improved from now on. It is clear that things need to be improved.
"Part of the evaluation is a thorough review of all available footage so that appropriate consequences may follow for those responsible for this outrageous behaviour.
"AZ is a civilised club where sportsmanship and norms and values are paramount. The club will do everything possible, together with the authorities involved, to identify these persons and to take appropriate measures."
The governing body’s disciplinary panel will wait for the relevant reports before deciding on any action, but the PA news agency understands that given the severity of the disorder, it could follow previous cases and an inspector may be appointed to investigate more thoroughly.
Given the extensive video footage of the ugly scenes the Dutch club could face heavy sanctions.
Hammers boss David Moyes, whose 87-year-old father David Snr was at the match, said: "I can’t explain what happened and why it happened.
"I can 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.
"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."
Additional reporting from PA