Argentina are still without a victory in the Copa America after the tournament hosts drew 0-0 with Colombia in Santa Fe on Wednesday.
Sergio Batista's team now require a victory in their final match against Costa Rica on Monday to ensure qualification for the second round.
Despite their 1-1 draw against Bolivia in the opening game, Batista again started with the attacking trio of Lionel Messi, Ezequiel Lavezzi and Carlos Tevez up front.
But it was Colombia, impressive in their first-round victory over Costa Rica, who dominated the first half. Chelsea target Falcao and Davro Moreno each came close, with Moreno in particular guilty of missing an open goal after Gabriel Milito's horror back-pass exposed Argentina's defence.
Once again, Argentina failed to get the best out of Messi, although Lavezzi should have done better in the 34th minute after the Barcelona forward put him through.
A similar pattern was repeated in the second half, as Tevez, Sergio Aguero and Gonzalo Higuain failed to test the Colombian defence. Pablo Armero came closest with a shot just across the face of goal in the 65th minute.
"No one expected this kind of game," Batista told the tournament's official web site. "Nothing comes out the way we expected.
"We have a game against Costa Rica, and we can have five points to qualify. We need to keep calm, think it is a final and come out with this mentality."
Argentina, with two points from two games, trail Colombia on four points. Bolivia, with one point, play Costa Rica, with nul points, on Thursday.
In the U.S., the tournament is being shown live exclusively on Spanish-language broadcaster Univision, with match highlights and live streaming also available on the company's website.
In the U.K., ESPN is broadcasting coverage of the tournament for the first time, a full list of live fixtures and highlights is available on the channel's website.
In addition, Google YouTube is streaming live matches to viewers in over 50 countries at youtube.com/copaamerica (not available in the U.K.). All matches are being screened live with English commentary including replays and highlights which are available on demand.