The American was subject to racist chants during his side's 5-0 KNVB Cup triumph at Den Bosch on Tuesday night with the home club revealing its horror at discovering the anti-social behaviour from their own supporters.
"A cup tie that was supposed to be played in an atmosphere of respect has left us scarred," the club said in a statement on its official website.
"These fans do not belong in the De Vliert (Stadium) and will face the toughest possible sanctions.
"(The fans) totally ruined weeks of preparations with monkey chants, throwing things at match officials and not showing respect for those on and around the pitch."
Altidore felt that educating ignorant fans would go a long way to eradicating racism in football.
"At the end of the day it's still alive, racism. All we can do now is try to educate ourselves, the young kids coming up, to be better than that," Altidore said.