Lautaro Martínez headed in the winner in the second minute of stoppage time, crushing England’s hopes after Anthony Gordon had put them ahead early in the second half.
Barco, 21, currently at Strasbourg and formerly with Brighton, is expected to join Chelsea.
He has appeared once at the tournament, coming on after halftime in a 3-1 group-stage win over Jordan.
The first half of Wednesday’s match in Atlanta was heated, producing 19 fouls as American referee Ismail Elfath struggled to keep control.
Bellingham, who has scored six times in the tournament, also had a brief exchange with Argentina captain Lionel Messi in the fourth minute after a foul on England’s Elliot Anderson.
“We were just talking about the foul,” Bellingham said afterward. “It wasn’t anything serious. People will probably make a big deal of it, but it was nothing.”