The in-form France playmaker bagged an excellent second-half brace to secure a 3-0 win on Sunday after Alvaro Negredo's eighth-minute free-kick set Manuel Pellegrini's team on their way to a seventh win from as many Premier League matches at the Etihad Stadium this term.
City are now six points behind leaders Arsenal, who are the next visitors to Eastlands.
However, before facing Arsenal, Pellegrini's men will look to address their wretched form on the road - which has brought just four points from six matches - in back-to-back games at West Brom and Southampton this week.
Nasri told BBC Sport: "Everything is fine at the moment; we had a tough first half but we came back with the best intentions, scored three goals and kept a clean sheet so it's a good afternoon for us.
"We have to improve our form away from home and we have two games to do this (in the next seven days). Six points is not a lot, in terms of the gap before we face Arsenal."
In light of the chastening 7-0 and 6-0 scorelines dished out to Norwich City and Tottenham respectively in City's last two home league games, Swansea might have feared the worst after Negredo's early opener.
Yet Michael Laudrup's team more than matched their opponents in the first half and Jonathan de Guzman spurned a glorious chance to level on the stroke of the interval.
Pellegrini again preferred Costel Pantilimon to Joe Hart in goal and the giant Romanian rewarded his boss with two fine first-half saves from Jonjo Shelvey.
"I'm very pleased because we won against a very difficult team, especially when they had possession," said the City manager.
"We didn't play very well in the first half but in the second we scored two goals and had more chances.
"Costel Pantilimon did very well; he didn't have too much work but when he needed to be there he really did well."
