The Rossoneri had enjoyed a dominant opening half hour that culminated in a well-taken Rafael Leao goal, but also saw Franck Kessie sent off for a debatable second yellow card.
However, with victory in sight, Milan were undone by a late Antoine Griezmann volley before Luis Suarez netted from the penalty spot in stoppage time after a Pierre Kalulu handball.
Frustration amongst the Diavolo was perhaps understandable, with question marks around the validity of Kessie’s second booking, whilst replays appeared to show that the ball hit the hand of Atletico’s Thomas Lemar prior to Kalulu in the build-up to the penalty.
It soured what was an excellent display of defensive solidity in the face of a tough match with a numerical disadvantage, whilst Brahim Diaz, Leao, Ismael Bennacer and Sandro Tonali in particular caught the eye.
After an eight year absence from the Champions League, Milan have adapted to a return to the top table of European football well despite having no points to show for it so far.
A difficult opening night trip to Anfield to face Liverpool saw the Rossoneri challenge the former Premier League winners and lead for a while, before the English club turned it around in the second half.
Tuesday’s defeat will be particularly galling given the circumstances, but there is enough evidence that Stefano Pioli’s side have the makings of a team that can challenge to get through the group.
Upcoming fixtures against Porto will be crucial, but despite defeat at the San Siro, the Diavolo will fancy their chances of getting a result against Atletico in Spain and marking their return to the Champions League with a memorable campaign.