The Turkish outfit, who are only in the tournament because of Fenerbahce's exclusion, snatched a 1-0 victory in the San Siro.
The Nerazzurri dominated the game but failed to get past Tolga Zengin in the Trabzonspor goal.
Argentinian Diego Milito was perhaps the worst culprit, spurning a number of gilt-edge chances.
The visitors took the lead when the Italians failed to clear from a corner and Ondrej Celustka turned a shot into the far corner.
In the other Group B fixture Joe Cole's new side Lille lost a two-goal lead at home to CSKA Moscow.
Seydou Doumbia scored a second-half brace to earn the Russians a 2-2 draw.