Okem Chime put us ahead before the Bees missed a hatful of first-half chances only to be punished as a late strike from Aaron Ibe sent the tie to penalties.
The Bees named a squad made entirely made out of scholars, graduates, and elite development players.
Roy Syla and Enrico Greco saw their spot-kicks saved as the visitors went through 4-3 on the night.
Barnet had the first opening of the match as Chime was denied by The Swans ‘keeper.
But Chime did open the scoring as he turned in George Murphy’s cut back.
Up the other end, Aymen Azaze made a superb stop to deny the visitors an equaliser as Olerain fired a shot at goal.
Chime had a chance to add to his tally but his effort was straight at the ‘keeper. Seconds later Jacob Adams denied Chime again this time with his knees as the striker was in on goal.
Syla was next to test Adam’s as the Swans ‘keeper did brilliantly to save a powerful effort from the edge of the box.
Azaze kept to his side by gathering Cani’s effort at the near post. The Bees dominated large periods of the half and should have been ahead by more than one at the break.
Just before the break, Mauro Vilhete saw an effort grazed the post on its way wide.
There was an early scare for the Bees in the second half as Michael Olarewaju poked just wide.
Up the other end, Murphy had an effort that went straight at Adams
It was a second-half that saw chances at a premium with the Bees controlling the possession.
With 11 minutes to play Chime almost wrapped it up but his effort was saved by the inspired Adams.
The visitors were inches from an equaliser after a clearance rebounded against Bradley Sweeney. Thankfully the ball rolled just wide of the post.
But with seven minutes to play Aaron Ibe fired past Azaze to equalise for the Swans.
With neither side able to find a winner the game headed to penalties.
Chime stepped up first and converted before Ibe levelled for the Swans.
Greco’s penalty was saved by Adams but Hattabi fired over leaving it one apiece after two each.
The next set of penalties were put away by Murphy and Cani. But Syla’s spot-kick was stopped as Sweeney put the visitors 3-2 ahead going into the final kicks.
Vasiliou kept us in it but Carvalho won it for the Swans as we headed out the competition.
Barnet: Azaze, Douglas, Hernandez, Syla, Edwards (c), Fujah (Greco ’85), Vasiliou, Murphy, Chime, Vilhete ( Titchmarsh ’45), Hercules (Kudrik ’65)