The Swans exited the EFL Cup in the third round after they were beaten 2-1 by holders Manchester City at the Liberty.
After a goal-less first half, the visitors did the damage after the break as Gael Clichy's shot deflected off Neil Taylor to round off a fine team move in the 49th minute.
Pep Guardiola's side doubled their lead 20 minutes later with Aleix Garcia's classy finish beating Kristoffer Nordfeldt.
Sub Gylfi Sigurdsson pulled one back in added on time as he got on the end of Modou Barrow's cross, and despite a late surge, Manchester City held firm to progress on the night.
Victory meant the visitors maintained their 100 per cent record this season, winning all nine of their games in all competitions.
The Swans again host Manchester City on Saturday as the focus turns to the Premier League.
Record signing Borja made his first start for Swansea City.
The Spaniard led the line in a Swans side that showed eight changes from the starting XI that went down 1-0 at Southampton last weekend - a game in which Borja came off the bench to make his debut for the club.
The other changes saw Kristoffer Nordfeldt, who was in goal for the 3-1 win at Peterborough in the last round, make his second appearance of the season while Angel Rangel, summer signing Mike van der Hoorn and Wales international Neil Taylor came in alongside Jordi Amat.
Leon Britton returned to captain the Swans while Jay Fulton - a scorer in the previous round - joined him and Jack Cork in midfield.
The final change saw Wayne Routledge make his first appearance since late August, with the winger providing support going forward.
SWANS: Kristoffer Nordfeldt, Angel Rangel, Mike van der Hoorn, Jordi Amat, Neil Taylor, Leon Britton (capt), Jay Fulton, Jack Cork (Leroy Fer, 55), Kyle Naughton (Gylfi Sigurdsson, 61), Wayne Routledge, Borja (Modou Barrow, 75).
SUBS: Gerhard Tremmel, Federico Fernandez, Stephen Kingsley, Fernando Llorente.
MANCHESTER CITY: Willy Caballero, Vincent Kompany (capt), Pablo Zabaleta, Fernando, Jesus Navas, Leroy Sane, Gael Clichy, John Stones, Angelino Tasende (Kevin de Bruyne, 58), Kelechi Iheanacho (Brahim Diaz, 81), Aleix Garcia (Tosin Adarabioyo, 90).
SUBS: Angus Gunn, Bacary Sagna, Fernandinho, Pablo Maffeo.
In a cagey opening to the game, it was the visitors who probed first as Angelino Tasende volleyed wide from inside the box from Pablo Zabaleta's cross.
The Swans were then almost gifted an opener as keeper Willy Caballero miss-hit a pass straight to Borja, and when the Spaniard fired a goalbound effort from 20 yards, Caballero redeemed himself by touching the shot over for a corner.
The Swans kept pushing, and a neat move involving Borja and Wayne Routledge send Neil Taylor racing into the box, but his low cross along goal was was snuffed out by Vincent Kompany.
At the other end, Manchester City went close to breaking the deadlock as Leroy Sane's low cross was almost knocked into his own net by Mike van der Hoorn, but keeper Kristoffer Nordfeldt's quick reflexes saw him save on the line.
That was the end of the action in the first half as both sides went into the break on level terms.
Half-time: Swans 0 Manchester City 0
The Swans were quick out of the blocks after the restart, with Borja's overhead kick floating wide with 45 seconds gone.
But that early threat was insignificant as the visitors took the lead in the 49th minute.
It was a superb team move from the cup holders, with the ball moving quickly from defence to attack. Eventually, Tasende's cross found Gael Clichy, and his shot beat Nordfeldt via a deflection off Taylor.
Francesco Guidolin made another attacking change just past the hour mark as Gylfi Sigurdsson took the place of Kyle Naughton.
And Sigurdsson was straight into the thick of it as he almost capitalised on John Stones' error, with the defender's heavy touch seeing him lose possession in his own box. Sigurdsson latched onto it, but he was denied by the feet of Caballero.
The Swans kept pushing, and Borja curled high and wide after he blocked Zabaleta's attempted clearance.
But, after 68 minutes, the visitors doubled their lead as the Swans failed to clear their lines. Jesus Navas found Aleix Garcia, and he sidefooted into the far corner of the net.
They weren't done yet, though, as sub Kevin de Bruyne went in search of a third, but Nordfeldt got down well to gather his rasping drive.
The Swans kept pushing to get themselves back in the tie, and Taylor was kept out by a fine reaction from Caballero after Sigurdsson's free-kick deflected into his path.
And they managed to pull one back in added on time as Sigurdsson got onto the end of sub Modou Barrow's low cross.
That was the end of the action, though, as the Swans bowed out of the tournament.