My bro owns 2010 City and we were so fed up with the exact issue u had xplained in ur poster. We went to Honda Breeze Multan and their Workshop incharge briefed us about this issue and he was the first guy at any dealership I found honest and coperative.
According to him new City's ECU is programmed to run on High Octane fuel instead of premier plus we have here at most of the pumps. And he gave us two options to fix this problem. One was to use 50/50 ratio of High octane and premiere plus and Second was to reprogram the MAP sensor reading required for premiere plus petrol. We went for this and reprogrammed the ECU for new MAP reading.
Believe me now we notice the change in cars pick up in 1-2-3 gears in between the range of 1000-2000 rpms. No power lag or anything, no knocking with or w/o AC.
I would recommend u to do the same. It will cost u Rs 1000 and time require for it is less than 5 minutes.