Argentina had to chase their Group A opener from the 47th minute when an error by midfielder Ever Banega allowed Bolivia to sneak into a shock lead against the hosts before substitute Sergio Aguero equalised half an hour later.
"They surprised us with a crap goal and we managed to draw thanks to Kun [Aguero], but we're sad because we didn't reach our objective. We did some things well but we have to keep improving," Messi told reporters.
Bolivia's point in the match in La Plata was the first they have ever picked up in a competitive match on Argentine soil.
"A night without altitude" was the headline in the daily Clarin in a play on words on the expression in Spanish which would better translate as a night without class.
Argentina played into the hands of a modest but well organised Bolivia, failing to execute coach Sergio Batista's passing game modelled on Lionel Messi's club side Barcelona.
"It's very difficult to play like Barcelona, but the idea is ball possession," Batista told reporters.
"We tried to play and be a team with a lot of the ball, but Bolivia put a lot of people in the middle and clogged the spaces. It was a difficult debut."
He explained that with the "player of the people" in his side he would get more football and less "vertigo" - meaning less headless running at the opposition defence.
Yet Tevez and Ezequiel Lavezzi, the two players flanking Messi in attack, did just that with the former earning some of the lowest match ratings in Saturday's papers.
Messi received an ovation from the crowd, but not for the reasons he would have liked, when he stood up to Bolivia's captain Ronald Raldes after a clash in the box.
The world's top player desperately wants to win them over like he has the Barcelona fans with his scoring exploits in Spain and Europe with 180 goals in 269 matches.
