The arch-rivals both failed to go through to the title round in the South American Under-20 championship being hosted by Argentina in the western Andean region of Cuyo.
Brazil, five times world champions and with 11 South American titles, lost 2-0 to Peru on Friday and finished bottom of Group B with four points from four matches in the first stage.
"It's embarrassing. It's very sad to return to Brazil with a sense of shame," coach Emerson Avila told reporters.
Argentina won their last match 3-2 against already qualified Colombia on Thursday but had already been eliminated by then, having picked up one point from their previous three games.
"We had good players but there was too much individualism," said Argentina midfielder Manuel Lanzini.
Chile are favourites after romping to four wins in Group A with Colombia and Paraguay also going through. Peru won Group B by one point from Uruguay with Ecuador also qualifying for the six-team championship group.
The top four qualify for the World Cup, from June 21-July 13, which Brazil have missed once before in 1979.
Argentina have garnered poor results since they won a record sixth world title in Canada in 2007.
Football pundits have blamed poor appointments to the coaching staff after the glory years under Jose Pekerman, who is now in charge of Colombia's fast-improving senior national team.
Pekerman steered Argentina to four world youth titles between 1995 and 2005 and his assistant Hugo Tocalli won the 2007 tournament after taking over but was not offered a new contract.
Success at Under-20 level helped Argentina to win the Olympic gold medal in 2004 and 2008 but they failed to qualify for last year's Games in London.