The Swans were denied a deserved point after Carlos Tevez's strike earned Manchester City victory in a game which saw Michel Vorm stretchered off in the remaining 30 minutes.
The Dutch keeper was injured while attempting to keep out the Argentinian's goal on the hour mark, with a suspected groin injury which could see him sidelined for around four-six weeks.
Michael Laudrup's side stood up to the Barclays Premier League champions, and left the stadium feeling they could and should have taken a point back with them to South West Wales.
Michu went close on a number of occasions, first being denied by Joe Hart after going in one-on-one with the English international in the first half just minutes after seeing a goal ruled out for offside.
Scoreless at the break, the Swans continued to hold out the hosts with their passing style and stern defence frustrating Roberto Mancini's side.
Aguero's superb strike then separated the sides, but the Swans again went close to levelling via Michu.
As it was, there was no reward for a brave effort, but the Swans - who lost 4-0 here in their first Premier League game last season - took home a lot of positives from their performance.
The Swans remained unchanged from the home win over Wigan.
It meant Michu continued up front with Jonathan de Guzman – once a target of Manchester City – in a midfield trio that also included Leon Britton and Ki Sung-Yueng.
Manchester City included former Swan Scott Sinclair among their substitutes as they looked to bounce back from their Champions League defeat to Ajax.
Manchester City: Joe Hart, Vincent Kompany (capt), Gael Clichy, Matija Nastasic, Alexsandar Kolarov (Mario Balotelli, ht), Micah Richards (Kolo Toure, 84), Yaya Toure, Samir Nasri, Gareth Barry, Carlos Tevez, Sergio Aguero (Joleon Lescott, 90+4).
Subs: Costel Pantilimon, Jack Rodwell, Scott Sinclair, Edin Dzeko.
Swans: Michel Vorm (Gerhard Tremmel, 66), Angel Rangel, Chico Flores, Ashley Williams (capt), Ben Davies, Leon Britton (Danny Graham, 72), Jonathan de Guzman, Ki Sung-Yueng, Pablo Hernandez (Nathan Dyer, 76), Wayne Routledge, Michu.
Subs: Garry Monk, Dwight Tiendalli, Kemy Agustien, Itay Shechter.
The Swans held their own for the opening 20 minutes against the champions, defending sternly and enjoying pockets of possession.
With Carlos Tevez and Sergio Aguero, the hosts were frustrated in the opening period, with Jonathan de Guzman's cross for Michu - which saw the Spaniard treated after a clash with heads with Micah Richards - the Swans' best chance so far.
The Swans did have the ball in the net after 36 minutes, Michu running onto Wayne Routledge's through ball before firing past Joe Hart into the top corner, only for the effort to be ruled offside.
City responded via Carlos Tevez, but the striker's effort was dealt with Michel Vorm.
Immediately the Swans headed up field, Routledge taking play on before being taking down by Richards. Pablo Hernandez latched onto the loose and, with advantage being played, the Spaniard raced down the right flank before his cross was cleared.
The Swans then created the best chance of the game after 40 minutes, with Ki's pass beating the City defence and sending Michu in one-on-one with Hart. The England international came to City's rescue, diverting the Spaniard's effort wide with his knee.
Half-time: Man City 0 Swans 0
Roberto Mancini made a change at the break, with Mario Balotelli replacing Alexsander Kolarov.
Aguero curled an effort wide after 33 seconds of the restart as City looked to up the pace.
Vorm did well to snuff out another City attack as Balotelli got onto the end of Samir Nasri's defence-splitting pass, but the Dutch keeper forced the Italian wide before the danger was cleared.
The Swans were continuing to frustrate the hosts, and when Hernandez'z cross was met by Michu, Hart spilled with the loose heading out to Ki, but his thunderous shot was blocked.
From the next attack, City broke the deadlock on the hour. Clichy spread possession to Tevez and, from 25 yards, the Argentinian fired past the diving Vorm into the corner of the net.
Disappointed by the goal, the Swans were hit by a setback to Vorm, who injured himself while attempting to keep out the effort.
He was stretchered off, with Gerhard Tremmel coming on in his place.
Michael Laudrup made another change with 20 minutes to go as Danny Graham replaced Leon Britton.
The Swans then went close to levelling, Ben Davies and Routledge linking up well down the left before de Guzman curled an effort wide with Hart stranded.
With 14 minutes left, Nathan Dyer came on for Hernandez in the Swans' final change.
The game came to a halt again with an injury to Micah Richards, who was stretchered off with a knee injury, and he was replaced by Kolo Toure.
That injury, along with Vorm's setback, meant 12 minutes of added on time.
Mancini replaced Aguero with centre-back Joleon Lescott as City looked to hold onto their lead.
And that they did, with the home rearguard having to deal with heavy pressure in the latter minutes.