The Barcelona star was pleased to come away with a result after enduring difficult playing conditions in La Paz.
Marcelo Moreno gifted the home side the lead midway through the first half, before Ever Banega restored parity shortly before the halftime whistle, and Messi was pleased to see his side get a draw in difficult conditions.
"It is terrible to play here at altitude, so a draw is a good result for us," Messi told reporters. "Every time you make an effort or play at high pace, you need time to recover.
"Some of the players had a headache and others felt a bit dizzy, but there was nothing wrong with me."
The Barcelona star then looked ahead to the remaining qualification games and stressed that the next two matches will be crucial.
"We now have two big games coming up," he said. "We host Colombia and we are traveling to Ecuador. They will be nice matches."
Argentina sits atop of the table with 24 points from 11 games, holding a four-point lead over second-placed Ecuador, which has a game in hand.