Messi scored from the penalty spot to salvage the draw for Argentina at the Minerao stadium in Belo Horizonte, cancelling out a first-half strike from Paraguay's Richard Sanchez.
"Frankly, it's a little frustrating not being able to get the win we need to take the next step," Messi said after the match. "We knew this would be difficult, we're still looking for the best group, for the best performance, to keep growing."
Argentina are still bottom of Group B with one point from two games but they could progress to the last eight with a win over third-placed Qatar in their final group game on Sunday.
"[The squad] is hurt by the situation because we can't manage to win a game, and we know today was key for us," Messi said. "We know we have to win the next game to advance."
The result ensured Colombia clinched top spot in the group on six points after they beat Qatar 1-0 earlier on. Paraguay are second on two points.
- Vickery: Messi ensures Argentina fight another day
"We know we'll be playing for our lives," Messi said. "It would be crazy if we can't advance from the group stage, when basically three [teams] advance from each group. I have no doubt we'll do it."
Argentina's caretaker coach Lionel Scaloni said his side had not played well and struggled to cope with the shock of conceding the first goal.
"Our first half was not good, we played with desperation at times and we couldn't control the play or create attacks. We had a very clear plan but couldn't execute it as we kept losing the ball," he told reporters.
"They scored with their first attack and that caused us a lot of uncertainty. For a team like Argentina, which feels like it always has to win, the first blow is hard to take, but we assured the players at halftime that it was just one goal."
Information from Reuters was used in this report.