Substitute Aguero struck in the third minute of injury time to secure the club's first victory in the competition and turn a frustrating night at the Etihad Stadium into a jubilant one. After conceding to Cani after just four minutes, it needed a Carlos Marchena own goal to haul them back into contention and the spark was still missing until Aguero's dramatic late intervention.
Mancini punched the air repeatedly in relief when Aguero struck knowing the goal had possibly kept hopes alive. The Italian said: "I hope this goal will be very important - it was very important to win the first game in the Champions League."
He added: "I think everything can happen in this group, for first place."
After Napoli and Bayern Munich drew 1-1 in Italy, City have gained ground and are three points behind the German side, the group leaders, halfway through the stage.
There was one side issue, however, as, three weeks after controversy over substitutions in the defeat in Munich, Mancini appeared to upset Adam Johnson by withdrawing him late in the first half.
The winger was replaced by Gareth Barry and shook his head as he left the field, but Mancini insisted there was no problem.
He said: "We didn't have many players in the middle and I wanted to move Yaya (Toure) behind Edin (Dzeko).
"Adam played very well but at that moment I had to do a tactical substitution.
"I spoke with him (afterwards) and he understood this."
Source: PA
Source: PA