A first half free kick from Antonio Marin handed the Croatian outfit all three points, sealing the hosts’ progression into the play-offs and condemning Paul Harsley's side to a third defeat in Group C and, ultimately, exit from the competition.
Needing to win in order to qualify for the play-off round, the pressure was on City from the off.
And the task was made all the more challenging by the game being played on a challenging, uneven surface which cut up easily.
However, that didn’t prevent the young Blues from making the brighter start, with Harsley’s side twice coming close in the opening five minutes.
Inside two minutes, a deft ball from skipper Tommy Doyle put Nabil Touazi clear on the left. The Spaniard chose to cut inside before firing in a low shot which Zagreb ‘keeper Renato Josipovic smartly saved.
City then created an even better opening two minutes later. Iker Pozo smartly ghosted through behind the hosts defence and squared to the waiting Touaizi but his close-range shot was blocked by the keeper one yard out.
Zagreb though showed their menace as a Vedad Radonja low drive tested keeper Gavin Bazunu before a Sipos snap- shot flew just wide of the left hand upright.
And City’s task suddenly became even harder on 20 minutes as Dinamo took the lead.
Doyle was adjudged to have infringed on the edge of the City box and Antonio Marin’s superb free kick gave Bazunu no chance and found the top right-hand corner of the net.
City were then inches away from levelling on 41 minutes. Amankwah found Morgan Rogers free on the right flank and his instinctive volley was arrowing in until Zagreb keeper Josipovic leapt to acrobatically tip the effort over.
City sought to further step up the pressure after the break bit found a physical, well drilled Zagreb side tough to break down.
On the hour though a superb through-ball from Braaf afforded substitute Keke Simmonds a clear sight of goal but, once more, the Zagreb keeper was equal to the task.
The woodwork then denied City a leveller.
Dutch winger Jayden Braaf showed his skill and vision to cut in from the before despatching a superb curling effort which clipped the bottom of the upright.
And City’s frustrating afternoon was summed up seven minutes from time as Simmonds saw his drive from three yards out blocked by the onrushing Josipovic after a wonderful raking pass from Lewis Fiorini.
How we lined up
What it means
City finish in third place in the group, meaning that we miss out on going through to the knockout stages. Atalanta and Zagreb finished in the top two positions to progress.
Our EDS side play our final match of 2019 on Sunday when we play host to Tottenham in a Premier League 2 encounter. Kick-off at the CFA is 12pm.