Korea's sliver-thin hopes of advancing to the next stage in the World Cup were dashed on Friday morning with a defeat at the hands of Belgium in São Paulo.
With one draw and two defeats, it is Korea's first winless World Cup in 16 years, and the first time it failed to advance to the round of 16 since 2006.
In the third and final match of the group stage Belgium, which had already advanced to the round of 16, beat Korea 1-0.
Jan Vertonghen of Tottenham Hotspurs scored at the 78th minute for Belgium, who had just 10 men on the pitch as Steven Defour of FC Porto was sent off just before the end of the first half.
Korea finished at the bottom of Group H with just one point. Belgium topped the group with nine points from three victories, and Algeria advanced with four points from one win and one draw.
Russia is also going home as it finished third in the group with two points from two draws.
The match between Algeria and Russia ended in a 1-1 draw, and Algeria was elated to be going through the knockout stage for the first time in its history.
This is the first time since the 1998 World Cup in France that Korea did not register a single win at the group stage. For three consecutive World Cups -- Korea/Japan in 2002, Germany in 2006, and South Africa in 2010 - Korea had at least one win.
Brazil and Mexico are through from Group A, the Netherlands and Chile from Group B, Colombia and Greece from Group C, Costa Rica and Uruguay from Group D, France and Switzerland from Group E, Argentina and Nigeria from Group F, and Germany and the U.S. from Group G.