Pep Guardiola’s side struggled to find any tempo against Huddersfield and must now try again at the Etihad Stadium to book their place in the quarter-finals.
A disappointing day all round for City saw unused substitute Raheem Sterling apparently targeted with a plastic bottle thrown by a supporter from the main stand as as he warmed up in the second half.
The bottle missed the England winger, leaving Guardiola to worry more about his team’s lacklustre display with star forwards including an off-key Sergio Aguero unable to break down the Terriers’ stubborn defence.
The Championship side began the game brightly and might have led early on through Rajiv van la Parra.
He was teed up on the edge of the City penalty area by Collin Quaner but his shot was too close to City goalkeeper Claudio Bravo.
But it was the visitors who should have led moments later as they were denied by some desperate goalkeeping and defending.
Nolito found himself in the clear but his shot was blocked well low down by Joel Coleman in the Huddersfield goal before Mark Hudson made a crucial goalline clearance from Jesus Navas’s follow-up effort.
Aguero lifted a shot just over for City from the edge of the area moments after being admonished by Guardiola for not pressing defenders quickly enough.
But then came two scares for the Premier League side, first when Jack Payne’s shot was tipped over by Bravo and then when Philip Billing found the City net but was denied the opening goal by an offside flag against team-mate Martin Cranie.
Nolito saw another shot deflected just wide as the game remained an end-to-end affair.
Van la Parra was then denied again by Bravo as the City keeper held comfortably onto his tame shot following a cross by Quaner.
The next chance fell to Aguero after a clever sequence of passes on the edge of the Huddersfield box, but the striker’s effort was saved smartly by Coleman.
Aguero was back in the action just a few seconds into the second half when he weaved into the Huddersfield box but saw a firm shot turned away well by the diving Coleman.
Some more fine footwork by the Argentine then took him away from two Huddersfield players but his pass for Fernandinho was overhit and Coleman gathered.