The Swans went down 2-1 to the Colorado Rapids in the first game of their tour of America.
Michael Laudrup's side were 2-0 down within 14 minutes after Andre Akpan and Kamani Hill, but Jonathan de Guzman pulled one back in the second half with a stunning free-kick from 25 yards.
Leroy Lita went close to pinching an equaliser late on, but his header bounced over after scraping the crossbar.
The Swans fielded two sides for each half at Dick's Sporting Arena - a venue based one mile above sea level - in Commerce City.
Laudrup, in charge for the first time since his arrival this summer, included new signing Michu in his first-half starting XI. The Spaniard played as the attacking member of a midfield trio also containing Leon Britton and Mark Gower.
Before kick-off, the whole stadium paid tribute to the victims of the tragic shooting in Aurora with a minute's silence, with skipper Garry Monk also placing a wreath on the halfway line to mark the Swans' tribute.
COLORADO RAPIDS: Steward Ceus (Ian Joyce, 76), Hunter Freeman (Davy Armstrong, 57), Tyrone Marshall, Scott Palguta, Luis Zapata (Tyson Wahl, 72), Jeff Larentowicz (Shane O'Neill, 57), Joseph Nane (Wells Thompson, ht), Jamie Castrillon (Tony Cascio, ht), Kamani Hill, Jamie Smith, Andre Akpan (Omar Cummings, 77).
SWANS: (First half): Gerhard Tremmel, Jazz Richards, Garry Monk (capt), Ashley Williams, Fede Bessone, Leon Britton, Mark Gower, Michu, Nathan Dyer, Stephen Dobbie, Danny Graham.
ATTENDANCE: 6,484
In a game played in conditions of 32C, the Rapids made a rapid start, with the Swans falling behind after just four minutes. Luis Zapata got onto the end of a through ball down the Swans' right flank and his pinpoint cross found Andre Akpan, who headed home past Gerhard Tremmel from eight yards out.
A cannon behind Tremmel's goal fired, as is tradition here at the Rapids stadium, and the home crowd were up on their feet applauding.
It was a superb start for the hosts, though Leon Britton went close to levelling with a 25-yard effort that just flew over the crossbar.
But as the Swans were working their way into the game, the cannon fired again. The Rapids struck after 14 minutes via Kamani Hill, the midfielder's 25-yard shot flying past the helpless Tremmel and in via the far post.
Danny Graham then went within inches of cutting the deficit as Nathan Dyer crossed along goal after Stephen Dobbie had pinched possession, but Graham just failed to connect with his diving header at the back post.
Michu then went close to his first Swans goal but his thunderous 20-yard volley was too high as the game ticked past the half-hour mark.
Graham also saw his curling effort swatted away by keeper Steward Ceus following Britton's neat chipped pass in what proved the last action of the first half.
HALF-TIME: Rapids 2 Swans 0
SWANS 2ND HALF: Gerhard Tremmel, Angel Rangel, Chico,
Alan Tate, Ben Davies, Kemy Agustien, Jonathan de Guzman, Andrea Orlandi, Wayne Routledge, Luke Moore, Leroy Lita.
As expected, Laudrup made ten changes at the break with Tremmel remaining in goal. That meant Chico got his first outing as a Swan, along with Jonathan de Guzman.
The Swans made a promising start, youngster Ben Davies curled in a teasing cross but the left-back's centre just evaded Leroy Lita.
In almost a replica move, Wayne Routledge crossed from deep but Lita and Luke Moore failed to connect at the back post.
Another Routledge delivery, this time a corner, found Chico, but the Spanish centre-back volleyed high.
The Swans' best chance of the game so far came with 72 minutes on the clock. Some neat play from Andrea Orlandi found Moore, who put Davies in down the left. His curling cross was met by the leaping Lita, but his header cannoned off the surface and over after scraping the crossbar.
Then the Swans finally got a goal back. It came following some fantastic individual play from Kemy Agustien and then Moore before Lita was fouled 25 yards out. Up stepped de Guzman, and the midfielder curled home a sublime effort past substitute keeper Ian Joyce.
"Come On City, Come On City" sang a small section in the crowd, with the Swans group also belting out "Hymns and Arias" in order to give their side an extra push in the final quarter of an hour.
Alan Tate almost levelled after de Guzman's free-kick found him in the box, but it took an inspired block from the Rapids defence to deny him.
Then, with three minutes left, Andrea Orlandi's scuffed shot was latched onto by Lita eight yards, but, despite beating the keeper to the ball, the striker's shot cruelly bounced the wrong side of the far post.
The Swans pushed hard for an equaliser, but time ran out on them as the Rapids ran out 2-1 winners.
The focus now turns to the friendly with Ventura County Fusion before ending the tour with a match against MLS outfit San Jose Earthquakes.