There was yet more international disappointment for Lionel Messi as his side lost to goals from Roger Martinez and Duvan Zapata in Salvador.
Argentina has reached four of the past five Copa America finals, losing them all, but will need to improve in its remaining Group B games against Paraguay and Qatar if it is to reach the showpiece in Brazil.
Maradona, who inspired Argentina to glory at the World Cup in 1986, was unimpressed with the lack of physicality on show against Carlos Queiroz's Colombia.
"You realise that Tonga can beat us," he said. "There is a prestige that we built with kicks, with punching.
"Let it be remembered that when we left Peru our bus was smashed up. What's left from all that? What does this shirt mean? You have to feel it, for f*ck's sake."
Argentina is seeking its first major international title since 1993.