But City, so much better at Eastlands compared with their form away from home this season, still have a chance of progressing to the semi-finals.
Even though Hamburg kicked off, City took the lead after only 36 seconds when Stephen Ireland slotted the ball home after being set up by Robinho.
Hamburg were unfazed though and poured forward creating chance after chance.
Shay Given saved David Jarolim's shot before the unmarked Mladen Petric headed straight at the former Newcastle United goalkeeper when he should really have scored.
In the eighth minute Given was forced to make a superb one-handed stop to keep Michael Gravgaard's close-range effort out but, from the resulting Piotr Trochowski corner, he was finally beaten when Netherlands international Joris Mathijsen headed the ball home.
The game continued at a frenetic pace with the Bundesliga side looking to attack at every opportunity.
Hamburg came within inches of taking a 20th-minute lead when Jonathan Pitroipa's floating header from a tight angle came back off the crossbar with Given beaten.
City were struggling to repel wave after wave of Hamburg attacks and Given once again had to come to their rescue when he pushed away Marcell Jansen's fierce shot midway through the first period.
In a rare City attack Craig Bellamy was denied by Frank Rost after being sent clear by Shaun Wright-Phillips but the ball should have been squared to Ireland who was unmarked and could have side-footed it into an open net.
Just before the break Given was at it again, saving Trochowski's shot with his knees.
The second half was a less open affair although Wright-Phillips tested Rost with a long-range effort just before the hour mark that the Hamburg keeper was equal to.
However, after Wright-Phillips was forced to hack the ball off the line, Hamburg took the lead in the 63rd minute. Micah Richards conceded a penalty when he handled the ball and Trochowski scored from the spot.
With 11 minutes left City were given a mountain to climb when substitute Jose Paolo Guerrero fired Trochowski's cross high into Given's net but, in truth, a two-goal advantage was the least Jol's side deserved for an enterprising display.