English Premier league star Sergio Aguero and captain Lionel Messi looked to have put Argentina on the road to a routine victory in Group B after firing the tournament favourites into a 2-0 first-half lead yesterday.
But a long-range strike from Nelson Valdez hauled Paraguay back into the contest before Argentine-born forward Lucas Barrios grabbed a dramatic 90th-minute equaliser.
The stunning comeback left Argentina in shock and could complicate their route through the knockout rounds in Chile.
"We lost control and the other team had four or five chances to get a draw," Martino told a news conference.
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"We had many chances to win," he added, saying that the team in the second half were "totally different from the side that played in the first half."
"I do not think we need to change anything. What we have to look back at the two games we played in the 90 minutes today."
- 'Like a victory' -
Paraguay goal hero Barrios was jubilant after his team's heroics.
"This group is so tough that getting a draw in the last minute against Argentina is like a victory," said Barrios, who plays for Montpellier in France.
Paraguay's other goalscorer, Valdez, paid tribute to the spirit shown by his team-mates.
"Individually we are less than Argentina, but as a team we are better than them," he said. "We needed a slap in the face at half-time.