Ondrej Celustka struck 14 minutes from time to leave Inter reeling and pile the pressure on new coach Gian Piero Gasperini after only three games in the job.
The Turkish runners-up, only in the competition after Fenerbahce were withdrawn because of match-fixing allegations, looked comfortable throughout before Celustka expertly hooked the ball in on the slide after Halil Altintop hit the bar.
Just before the goal, Inter substitute Diego Milito spurned two gilt-edged chances when his close-range effort was saved and then his header went over but generally the hosts were poor in their opening Group B clash.
Gasperini has now lost his first three matches in charge, including the Italian Super Cup defeat by AC Milan.
"We are not in a lucky moment, this defeats leaves us with lots of regrets but the team know they have given a lot and put in a decent showing," Gasperini told Sky TV.
"We are a team that will definitely get better, we have potential, will will get injured players back. The will and the determination of the players is clear. Moratti has always really supported me."
The coach has though already been criticised in the media by the club's owner Massimo Moratti, who has seen bosses Jose Mourinho, Rafa Benitez and Leonardo leave since their 2010 treble as last season went sour.
LITTLE DIFFERENCE
Moratti has also been left red-faced after the club failed to realise that new striker Diego Forlan was ineligible for the Champions League because of European action this term for Atletico Madrid.
Former Genoa coach Gasperini, inexperienced at the top level, abandoned the three-man defence that flopped in Sunday's opening 4-3 Serie A defeat at Palermo and reverted to their traditional four at the back but it made little difference.
A spark was lacking and the hosts only really came to life midway through the second half when Mauro Zarate had a shot saved at the near post and then strike partner Giampaolo Pazzini failed to connect with the goal at his mercy.
Wesley Sneijder wasted another free kick just after the break and Inter continued to labour with their slow build-up play giving the visitors ample chance to cover any gaps.
Disjointed Inter were second in Serie A last season behind Milan and few fans expect the current crop to challenge for a title in Europe this campaign.
Wednesday's performance will reinforce that view and send odds tumbling of Inter going through a fifth manager in just over a year even if Trabzonspor failed to offer much threat until Czech Celustka's goal.
The visitors, who had two players suspended and coach Senol Gunes banned from the bench, had goalkeeper Tolga Zengin to thank for some smart saves late on.
Inter next travel to CSKA Moscow on September 27 when Trabzonspor host Lille, who drew 2-2 at home to the Russian side in their group opener on Wednesday.
