Dzeko struck twice in a blistering start by the Blues before a deflected Yaya Toure strike sealed a comfortable 3-0 win over Aris Salonika.
After drawing 0-0 in Greece in the first leg, it meant for an easy passage into the next round to face Dynamo Kiev.
Since his big-money move from Wolfsburg last month Dzeko had scored just two goals in his first eight games for City – both in the FA Cup against League One Notts County.
But the Bosnian striker, 24, began to live up to his £27million price-tag as he produced two well-taken strikes inside the opening 12 minutes.
“Edin played well, he scored two goals, and for him it’s very important,” Mancini told ESPN.
“It was important that we started very well in the game. The first half-an-hour, 40 minutes we played very well, scored two goals and had other chances to score.”
Mouth-watering
Dzeko, Mario Balotelli and top-scorer Carlos Tevez started together for the first time in a mouth-watering forward line that blew Aris away early on.
And although the visitors never looked like mounting a fightback, Mancini insists victory was not assured until the third goal in the 75th minute.
“In the first half they played very well but second half, when we were so tired, I think that we had some problems with the balance,” added the Blues boss.
“It was the first time so they need to play (together) again.
“After the Toure goal we could relax but before, no. In football you can never say never.
“If they scored one goal they would have opened the game.”
It was City’s seventh straight home win but Mancini is refusing to look too far ahead despite the Blues’ next three games also being at Eastlands, including the FA Cup fifth-round tie with Aston Villa.
“On Sunday we play Fulham and at the moment Fulham are playing very well,” he added.
“A big problem is that we have four or five important players injured and I hope we can recover two players for the next game. But I think we must take one game at a time.”
City then travel to Kiev on March 10 and Mancini is expecting a tough test.
“I have played against them a lot of times, they are a big team, one of the best in Ukraine,” he said.
“They always play in the Champions League and have lots of experience so it will be a very difficult game.”
Read more from the original source:
Roberto Mancini Hails Two-Goal Dzeko