David Silva missed a penalty before Carlos Tevez opened the scoring before goals from Rickie Lambert and Steven Davis gave Southampton hope of a shock victory.
But Bosnian Edin Dzeko restored parity before Nasri scored an 80th minute winner.
Match-winner Nasri was happy that his side managed to come back to win the game.
He said: "It was like the last game of the season (when City beat QPR 3-2 to win the title), we've started the same and I hope at the end it will be the same result for us. It was a difficult game.
"Southampton played really good football. It reminds me a little bit of Swansea last year, it was difficult but at the end we got three points," Nasri added on Sky Sports 1.
"Sometimes it's a little bit difficult when you miss the first chance of the game, it can make the confidence a little bit low and they punished us. But I thought we showed great character.
"We didn't panic. We said we can do it, we did it last year and for the remainder of the season we can do it."
Manchester City manager Roberto Mancini believes his side have to learn how to close games out if they are to maintain last season's success.
"I hope it's the last day like this. It's important we won this game, because the first day is always difficult," Mancini told Sky Sports 1.
"It is important we have character. We understand that we have to close the game before because we had many chances to close out the game and we didn't do it.
"It is normal for us. It happened last year two or three times, but I think today (Sunday) it was only because it was the first game. We've only been back for two weeks."
Nigel Adkins was happy with the way his charges applied themselves but stressed that his side must find a way to win games in the Premier League.
"We've played against the new champions. Our defenders have just played against the best forward line they've ever played in their lives and I think manfully they've put a good performance in today (Sunday)," said Adkins.
"I think they only conceded 12 goals at home last season. We've just scored two against them today (Sunday).We knew it was going to be challenging but I thought we utilised the group of players we have intelligently to try and get something from the game.
"I give great credit to our players , they've put a shift in again. I think that's going to give us a lot of belief and we have to find ways to win games of football. We've got to be intelligent to give ourselves an opportunity to win because that's what ultimately it's about.
"We try to play football the right way, we try and pass it but we have to find ways to win games in the Premier League.
"We know we're going to have to defend well in the Barclays Premier League, especially against the quality of opposition we've faced today (Sunday). We'll learn the lessons from today's game.
"We have to keep our belief strong that we can come away from home and win points because that's what we have to do."