Despite conceding the opening goal when Fabio Borini neatly finished, a spectacular Yaya Toure leveller, followed by a well taken goal by Nasri and a late Navas strike, gave City the win.
"We want to win everything," Nasri is quoted as saying in the Metro. "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."
The game was looking like slipping away from City as Sunderland went in at the break with the lead.
However, an improved second-half performance from Manuel Pellegrini's side was enough to secure the first, of what Nasri hopes, is many trophies.
"In the second half, we came with intention and scored three goals," he said.
"I hope this cup is going to bring some others. We were still confident [at half-time]. We said we needed to stay calm and remain focused, play higher up and play with more tempo and that’s what we did."
For a while it was looking like third time unlucky for Nasri who has suffered cup final defeats twice at Wembley.
He was part of the Arsenal side that surprisingly lost to Birmingham in the 2008 League Cup final, as well as losing to Wigan last year with City in the FA Cup.
But when the former Marseille man netted his goal, the game only looked like going in one direction, much to his delight.
"So much joy, so much pride as well. I lost the two finals that I played here before. Today it was really important to win."
City will now turn their attention to the FA Cup, as they bid to swiftly return to Wembley for a semi-final - providing they can avenge last season's defeat to Wigan.