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The Bolivians might have shocked the albiceleste in a World Cup qualifier two seasons ago with a 6-1 win in La Paz - but that was at high altitude.
Here, there could be no excuses as Edivaldo Rojas gave the Bolivians a deserved whiff of a first ever win on Argentinian soil after 11 losses before Sergio Aguero rescued a point with a crisp late volley.
"They put men behind the ball, parked the bus and we could not find a way through," admitted Messi, who despite his heroics with Barcelona in scoring over 50 goals last season has never quite reached the heights when he has donned the national shirt.
"It's not what we were hoping for and we are sad.
"Now we know the matches we have to come in the group (against Colombia and Costa Rica) are ones we just have to win," he added.
Bolivia were determined not to be the fall guys in Group A and this draw means they can also hope to get through from the group phase.
Meanwhile, Messi said Argentina must go back to the drawing board and "see what we did well and sift through what we did badly and so try to get back to winning ways.
"We must keep calm. We haven't started off as well as we hoped but now we simply must up our game in the coming matches."
Aguero said he had to credit Bolivia's fighting spirit.
"Now we have to do a bit better as they made it hard for us though I thought we started off all right before they got the goal," said the Atletico Madrid striker and son-in-law of former Argentina coach Diego Maradona, who dedicated his goal, as ever, to his family.
Argentina's other attacking spearhead, Carlos Tevez, warned, meanwhile, that Argentina had work to do if they did not want to fall flat on their faces as they seek to end a barren trophy run stretching back to the 1993 win they managed in Ecuador.
We knew this would be a tough Copa," said the Manchester City forward.
"We need to keep calm and keep things in perspective as if we lose heart it will be worse for us.
"Today we were short on goals, we didn't gell well in attack or have much mobility but we do know what we are trying to achieve and how we want to approach our game," he insisted.
Argentina, 14 times continental champions - a record they share with Uruguay, with Brazil having netted just eight but four out of the last five nonetheless - now have five days to plot a way past unpredictable Colombia on Wednesday at Santa Fe before they go up against Costa Rica, special guests in the absence of original invitees Japan.
