US Edition With David Silva involved as well, it provided a fearsome forward line the Greeks were incapable of resisting. As City took their tally to 19 goals in their last five home games, Dzeko took the honours with a double inside the first 12 minutes.
However Mancini does not think he can go for broke all the time. "I thought we did well and in the first half I was very pleased," said the Italian.
"The problem comes when we don't have the ball. If we don't close down every situation, it could be difficult for us.
"We can play this formation but not often, unless we improve."
Dzeko's efforts doubled his previous tally since a £27 million move from Wolfsburg last month.
The Bosnian should have had a hat-trick too after being sent through by Silva in the final minutes of the first half.
However, the chance went begging when Michail Sifakis robbed him as Dzeko attempted to go around the Aris goalkeeper, and it was left to Yaya Toure to complete the scoring with a deflected effort 15 minutes from time.
It means City now travel to Ukraine on March 10 for the first leg of a tie against Dinamo Kiev featuring striker Andriy Shevchenko.
"They have a lot of experience," said Mancini. "Dynamo have always played in the Champions League and we know this will be a very hard game because they are a good team.
"There is no point looking any further forward than that because there are still a lot of big teams left in this competition."
Mancini claimed Balotelli is still not firing at 100 per cent after a recent knee injury, although there were signs of improvement and the Italian did hit the post with one second-half effort.
However, with injuries already ravaging his squad, Mancini can only hope the hip problem that forced Vincent Kompany off before the break proves not to be too serious.
"We won't know what has happened until tomorrow when we see what the situation is," said Mancini. "We have a lot of injuries at the moment, so I hope it is not serious and he will be available for Sunday."
Aris coach Ioannis Michalitsios was refreshingly honest as he assessed his side's downfall, even though the Greek outfit had gone into the tie level after the first leg on home soil.
"We lost to a better team," he said.
"We found ourselves two down in the first few minutes, which obviously knocked us back. Given what happened, the eventual outcome could have been a lot worse.
"In order to knock Manchester City out we needed a perfect performance and for City to make a lot of errors. That did not happen.
"City are a better team that most in Europe and the favourites to win the Europa League this season."