Czech defender Ondrej Celustka scored in the 76th minute at the San Siro following the rebound of a shot from Halil Altintop that hit the crossbar.
Trabzonspor only gained a spot in the group stage after Fenerbahce was removed by the Turkish Football Federation because it is under suspicion in a criminal probe into match-fixing.
The loss deepens an early season crisis for Inter, which has lost all three of its fixtures thus far and is lacking order under new coach Gian Piero Gasperini.
Inter was beaten 2-1 by AC Milan in the Italian Super Cup last month and lost 4-3 at Palermo in its Serie A opener Sunday.
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