The Frenchman suffered Wembley defeat with Arsenal in the 2011 final and again in City's shock 1-0 FA Cup reverse against Wigan Athletic last year.
The early signs were ominous for Nasri on Sunday, with Fabio Borini's deft finish handing the underdogs the halftime advantage.
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But stunning strikes from Yaya Toure and Nasri in the space of two second-half minutes turned the game on its head, before Jesus Navas added late gloss with the third.
Nasri is now hopeful City can use the triumph as a springboard for quadruple success, with Pellegrini's men still in contention to win the Premier League and FA Cup, while they will need to turn around a two-goal deficit against Barcelona in their Champions League tie.
"[I have] so much joy and so much pride because I lost my two finals here and it was really important today to win," he told Sky Sports. "Today was important to win, first half it was memories of the game against Wigan. In the second half, we came with good intentions and scored three goals. I hope this will bring some others [trophies].
"We want to win everything. We're going to compete for the league, the FA Cup and we're going to try to make something in the Champions League. I hope this is going to bring confidence, and we'll fight until the end."
Toure started City's comeback with a stunning 30-yard effort that bent into the top corner and the Ivorian ranks it as the best strike of his career.
"I think it was [my best goal]," Toure said. "We needed to win today, it was very important.
"Sunderland made it difficult for us in the first half. It's unbelievable and we deserve it. The final is only one game, you need to enjoy it, and today we showed we have a great team."
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- Yaya Toure
- Wigan Athletic
- Fabio Borini