In a repeat of the 2023 final in which City emerged victorious in Istanbul, Pep Guardiola's side struggled to break down an impressive Inter line-up who troubled them on numerous occasions, most notably via a late chance for Henrikh Mkhitaryan, who put his shot over.
Phil Foden and Ilkay Gundogan went close near the end for City, but former Manchester United defender Matteo Darmian had perhaps the best chance of the game when he back-heeled at goal when a more conventional shot looked the better option.
Celtic eclipsed their biggest victory in the group stage era with a 5-1 win at home to Slovan Bratislava as Brendan Rodgers' side made a dream start on Wednesday (Thursday AEST).
Liam Scales headed the hosts in front in the 17th minute, but it was after the break that the floodgates opened, beginning with Kyogo Furuhashi turning home Nicolas-Gerrit Kuhn's driven cross.
Arne Engels made it three in the 56th minute after Alistair Johnston had been felled with a high challenge from Danylo Ihnatenko, before Daizen Maeda and substitute Adam Idah added further goals to seal a famous win.
Elsewhere, Paris Saint Germain inflicted heartbreak on Champions League debutants Girona as goalkeeper Paulo Gazzaniga's last-minute error gifted the Ligue 1 champions a 1-0 victory at the Parc de Princes.
With the team who were in the Spanish fifth tier as recently as 1999 looking set to earn a famous point, PSG defender Nuno Mendes stole away down the left and sent across a low ball that deflected off the outstretched leg of substitute Alejandro Frances before squeezing through the arms and body of Gazzaniga for an own-goal to save the home side's blushes.
Last season's runners-up Borussia Dortmund got their campaign off to a perfect start with a 3-0 win away to Club Brugge, though Nuri Sahin's side left it late to seal victory in Belgium.
Dortmund's Jamie Gittens scored a double in his side's 3-0 win over Club Brugge. (AP PHOTO)
The game was goalless going into the final 15 minutes when England Under-21 winger Jamie Gittens scored twice to effectively kill the game, the first a drive that deflected off two defenders before looping into the corner, then following it up with a fine effort after an impressive step-over.
Summer signing Serhou Guirassy added a third in the fifth minute of stoppage time for the Bundesliga side.
Sparta Prague ran out 3-0 winners at home to Red Bull Salzburg, whilst Bologna's Champions League debut ended in a goalless draw at home to Shakhtar Donetsk, for whom Heorhii Sudakov had a penalty saved by goalkeeper Lukasz Skorupski in the fourth minute.
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