Stefano Denswil's header in the 90th minute looked to have given the hosts their first win in this season's competition, but referee Jonas Eriksson awarded the Rossoneri a stoppage-time spot-kick after ruling that Mike van der Hoorn had brought down Mario Balotelli inside the area.
Balotelli scored the penalty kick to preserve Milan's unbeaten record after two games, leaving Ajax third in the group with one point.
"It was ridiculous that a penalty was given against us. It cost us two points," De Boer raged in his post-game interview.
"There are always moments of contact. It is the right time to let go. Van der Hoorn left him at the right moment.
"Eventually, I can live with a draw, even if the penalty is disappointing."