After losing 1-0 to Sweden in its previous match, the U.S. was eliminated from reaching the final. Head coach Tom Sermanni made a number of changes to Monday's lineup.
Abby Wambach started the contest on the bench, while Amy Rodriguez and Tobin Heath were unused substitutes and watched as the Americans fell behind 3-0 at halftime.
Denmark's Katine Veje opened the scoring after 24 minutes, and Nadim added two more before the break to give the Danes a commanding lead.
The U.S. mounted a comeback in the second half with goals from Christen Press, Sydney Leroux and Megan Rapinoe to get to within 4-3 with 20 minutes to play.
But as the Americans threw players forward in search of an equalizer they were caught on the break and Karoline Nielsen put the game away with a goal in stoppage time.
The result leaves the U.S. on the bottom of the group with just one point from three games.