City recorded a 3-1 victory over Sunderland to win the Capital One Cup final.
The first trophy of the Manuel Pellegrini era was won the hard way after City fell behind to Fabio Borini's superb first-half opener, but the Barclays Premier League title challengers roared back after the break, with Yaya Toure's stunning 30-yard strike pulling the scores level and man of the match Nasri notching a crisp second withing two minutes.
Jesus Navas added gloss late on with City's third, as the first part of a realistic treble - and possible quadruple - was ticked off.
"I feel so much joy, so much pride as well," Nasri told Sky Sports 1. "It was really important to win.
"In the second half we came with better intention and we scored three goals. I'm really happy, I hope that this cup is going to bring some others."
City will now hope to add the league title to their list of honours this season, while they are also in the quarter-finals of the FA Cup. The Champions League represents a more fanciful aim, with Pellegrini's men trailing Barcelona 2-0 after the first leg of their last-16 tie, but Nasri is not giving up hope.
"We want to win everything, we're going to compete for the league, for the FA cup, and we're going to try and make something happen in the Champions League - it's going to be difficult," he said.
Nasri had wound up on the losing side in his previous two Wembley finals, most recently in last year's FA Cup final against Wigan, and the France international admitted memories of last May came flooding back when Sunderland took the lead.
"Our first half, there was memories of Wigan," he said. "We said [at half-time] that we need to stay clam, to remain focused and play our football."
Toure's lofted, first-time strike from distance - surely one of the finest ever scored at the national stadium - was the catalyst for the City fightback and the Ivory Coast star admitted it could be his best ever goal.
"I think yes," he said. "It was important as well.
"We needed to win today. It was very important. The final is only one game and you need to enjoy it - but you need to win."
The victory marked Pellegrini's first major trophy in European football and the Chilean was understandably delighted to break his duck.
"I'm very happy," he said. "To win the first trophy I think is important for us all. For the players, for me and for the staff - everyone.
"It's very important, because at an important club you must win trophies."
Asked about his side's disappointing first-half performance, he added: "We were not doing things well. Sunderland played a very good match.
"In the second half we changed it and scored two beautiful goals and we had the patience to win. The second half we were the better team."
City captain Vincent Kompany was delighted to lift the trophy at Wembley, and said: "It's the best stadium, for me it's the best in Europe, maybe even the world, and lifting the trophy here is something special.
"We never take anything for granted and we'll enjoy every moment.
"I think we should be hungry for more. We've achieved something great for the club and we need to carry on."
Sunderland captain John O'Shea, meanwhile, admitted defeat was a bitter pill to take but conceded the better team were going home with the trophy.
"We're terribly disappointed. They only way you enjoy a cup final is by winning it," he said.
"They've scored a great goal to get back into it, he's stuck it in the top corner from 30 yards out and then we've lost a bit of organisation and it's cost us a second goal.
"It's not a nice place now and we have a huge test for the rest of the season.
"But credit to them - they're deserving winners."
Black Cats boss Gus Poyet was sanguine in defeat, able to take comfort from the fact his players could not have given any more.
"We had a go, we were 1-0 up, we knew everything had to go for us. But a little foul not given, a wonder goal from Yaya Toure and then an incredible finish from Nasri...
"I'm proud of the players, proud of the fans. I can promise them we gave the best shot we had today.
"To beat us today City had to score two wonder goals.
"Defeat today, I hate it. I hate losing, but I'm proud of the players."