"This never would have happened if they cared about lives over productivity," the sister of one of the victims commented on social media.
The company says its team had "worked quickly" in response to the tornado.
The roof collapsed as the storm hit the warehouse on Friday.
Kelly Nantel, an Amazon spokesperson said in a statement the company is "deeply saddened" by the deaths.
One of those who died, Clayton Cope, 29, spoke to his family on the phone shortly before the building in the town of Edwardsville, Illinois was struck.