The Swans were made to rue missed chances as they exited the Capital One Cup with a 1-0 defeat at Hull City.
David Meyler's first-half goal proved the difference between the two sides, but the Swans saw plenty of chances go begging at the KC Stadium.
In an action-packed opening 45 minutes, Eder saw an effort hit the post while Gylfi Sigurdsson was denied by a goal-line clearance from Curtis Davies, and Wayne Routledge hit wide after beating the Hull offside trap to race through on goal.
The opportunities piled up for Garry Monk's side, but the hosts managed to find the elusive opener as Meyler hit home from close range after Kristoffer Nordfeldt had saved Shaun Maloney's initial header.
Monk's men dominated possession during a frustrating second period, but their efforts to find an equaliser were stifled by the home defence with Routledge being denied a goal for being offside.
The Swans made ten changes to the starting line-up for the Capital One Cup third round tie.
Gylfi Sigurdsson was the only player in Garry Monk's starting plans from the side that took on Everton last weekend.
That meant Swedish international Kristoffer Nordfeldt, French left-back Franck Tabanou and Portuguese striker Eder made their second starts since joining in the summer.
Leon Britton captained the Swans who also included South Korea skipper Ki Sung-Yueng in midfield.
Eldin Jakupovic, Curtis Davies, Ryan Taylor (Moses Odubajo, 59), David Meyler, Harry Maguire, Jake Livermore (Sam Clucas, 69), Shaun Maloney, Chuba Akpom, Isaac Hayden (Tom Huddlestone, 83), Andy Robertson, Ahmed Elmohamady (capt).
Allan McGregor, Alex Bruce, Tom Huddlestone, Sone Aluko.
Kristoffer Nordfeldt, Angel Rangel, Kyle Bartley, Jordi Amat, Franck Tabanou (Kyle Naughton, 71), Leon Britton (capt), Ki Sung-Yueng, Matt Grimes (Jonjo Shelvey, 57), Gylfi Sigurdsson, Wayne Routledge, Eder (Bafe Gomis, 64).
Gerhard Tremmel, Kyle Naughton, Federico Fernandez, Jack Cork, Jefferson Montero.
The Swans were presented a fantastic opportunity to get off to a flying start inside three minutes when Eder prodded over the bar from six-yards after getting on the end of Franck Tabanou's inviting free-kick into the box.
The hosts then had a chance of their own seven minutes later as David Meyler saw a 20-yard drive parried over the bar by Swans stopper Kristoffer Nordfeldt, before Matt Grimes headed over at the opposite end.
Garry Monk's men looked to have broken the deadlock after 15 minutes, only to see two glorious chances go begging.
After Eder charged down Hull goalkeeper Eldin Jakupovic's clearance onto the post, the striker played in Gylfi Sigurdsson, who rounded the goalkeeper but saw his shot cleared off the line by Curtis Davies.
But the Swans were in again moments later as Wayne Routledge raced through on goal, beating the opposition's offside trap, only to drag his effort wide of the post.
In a first half full of chances, Hull then went close as Nordfeldt displayed quick reactions to deny Chuba Akpom, while Jakupovic was on hand to prevent Angel Rangel's point-blank range header from nestling into the back of the net.
The opportunities on goal were piling up for Monk's men as Routledge headed over the bar ten minutes before the midway point, while Sigurdsson's left-footed effort went narrowly wide of the far post following neat link-up play with Eder.
But for all the openings the Swans had engineered, it was the hosts that opened the scoring on 41 minutes when Meyler poked home from close range after Nordfeldt had denied Shaun Maloney's initial header.
HALF-TIME: Hull City 1 Swans 0
In contrast to the first 45, chances were few and far between early on in the second period.
Shaun Maloney was first to test the hands of either goalkeeper with a fizzing free-kick on 50 minutes that Nordfeldt punched wide, while Ki Sung-Yueng fired over the bar after been teed up on the edge of the box by Routledge shortly before the hour-mark.
Routledge also saw his effort ruled out after he was adjudged to have been fractionally offside.
With the tie turning into a scrappy affair, Monk introduced Jonjo Shelvey, Bafe Gomis and Kyle Naughton into the fray in an attempt to rescue Swansea's Capital One Cup campaign.
With just under 15 minutes left on the clock, Kyle Bartley saw a glancing header cleared off the line by Andy Robertson, while Sigurdsson fired over from 18 yards.
The Swans dominated possession throughout the second period but struggled to create the kind of opportunities that were so frequent in the first half.
And that meant Hull progressed to the fourth round as the Swans now focus on Saturday's trip to Southampton.