Veteran USA striker, Abby Wambach, scored the only goal of the game off a corner-kick in the 45th minute of the first half.
Things went from bad to worse for the Falcons when defender Sarah Nnodim was sent off with a second yellow card following a late tackle on Sydney Leroux.
The result means the Falcons, who finished the competition with just one point and ended bottom of their group, have now failed to make it out of the group stage in four consecutive World Cups.
In the group’s other game, Australia held Sweden to a 1-1 draw, joining the United States in the round of 16.
Meanwhile, Africa’s other representatives, Cameroon qualified for the next round after they defeated Switzerland 2-1.