Argentina's win over the Asian champions, thanks to an early goal from Lautaro Martinez and a late strike from Sergio Aguero, has put them into a quarter-final against Venezuela in Rio de Janeiro on Friday.
"We played a good game and we won, and that was what mattered," Messi said.
"We needed a game like this to gain some confidence and calm."
"As we play more games the team grows each one and that game was good for that."
Argentina came into the match under fire after losing their opener 2-0 to Colombia and then being held 1-1 by Paraguay.
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Too many of their top players have failed to reproduce their club form at international level but they were at least creating chances up front against Qatar, even if they were vulnerable at the back throughout.
The score did not reflect the number of chances - Argentina had 17 shots on goal to Qatar's four - but neither did it flatter the Qataris, who matched Argentina for most of the first half before running out of steam.
But while no one should draw too many conclusions from a victory over Qatar, who finished with one point for the tournament, the win sets Argentina up for a run at the title they have not won since 1993.
Coach Lionel Scaloni said he was content with the performance and delighted to still be in with a chance of silverware.
"Of course there are things we can improve on but we're satisfied," he said.
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"We always tried to play football and pressure them high up the pitch. I think the second half was very good.
"The message has to be that as long as we're in the Copa America we need to keep pushing forward."
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