The game appeared to be petering out to a 1-1 draw before the substitute intervened on 87 minutes.
Mancini started in attack with Sergio Aguero and Carlos Tevez but turned to the Bosnia and Herzegovina international in the closing stages and he delivered with a well taken strike.
Dzeko told Sky Sports 1: "The goals are my message. That's the only thing.
"It's not the first time [he has scored the winner] but it is a good feeling of course."
But after falling a goal behind to Spurs he feels the team are showing a great deal of solidarity.
"Even when we are losing we come back. I hope next time we are winning 1-0 and then go on and win the game,” added Dzeko.