The Rossoneri's attack fell short on a rainy, cold, and windy evening in the Netherlands.
Feyenoord's opening goal came off a long-driven effort from Igor Paixao, with Milan goalkeeper Mike Maignan failing to parry the ball out of danger as it slid across his hands into the back of the net. It was a fluke of an effort and a chance that the France international will want back.
Pulisic, meanwhile, completed 18 of 22 pass attempts, registering just 36 touches on an off evening for the winger.
Musah will be eligible to play in Leg 2.