Messi, 34, had previously tasted defeat in three Copa finals and one World Cup final with Argentina, with his critics, at home and abroad, often questioning his ability to lead his country to silverware.
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However, at the fifth time of asking, Messi finally won a major final with Argentina as Angel Di Maria's 22nd-minute goal at the Maracana ended the Albiceleste's 28-year wait for a trophy.
"I was close many times," a visibly emotional Messi told reporters after the match. "I knew it would happen eventually. I am grateful to God for giving me this moment, in Brazil against Brazil. I think He was saving this moment for me.
"I still don't think we are aware of what we have done, beyond becoming champions. Now we're really happy, celebrating, but this is a game for the history books, beating Brazil in a final in Brazil.
"It's crazy. I can't explain how happy I feel. I've been sad many times [with Argentina after tournaments] but I knew it would happen and there's no better moment. This team deserved it."
At full-time, the Argentina players raced toward Messi and threw him in the air in recognition of his role in their run to the final.
Messi, who is a free agent after his Barcelona contract expired on June 30, also shared an intimate moment at full-time with Brazil's Neymar and Argentina coach Lionel Scaloni, who he later paid tribute to.
"It's to the merit of [Scaloni] because of everything he's done and what he's built," the forward said. "The process with him started three years ago and it's been constant growth. He knew how to build a spectacular group, a winning group. He deserves the recognition. It's been a long time since Argentina were champions of South America, and we've won it again under him."
Messi has won everything in the club game with Barcelona and has been named the best player in the world on six occasions. Success with Argentina, though, had always eluded him.
He won the Under-20 World Cup and an Olympic gold medal with the U23s but tasted defeat in the 2007, 2015 and 2016 Copa America finals and was on the losing side against Germany in the 2014 World Cup final in Brazil.
Messi, who broke Javier Mascherano's appearance record for Argentina during the tournament, with 151 caps, now wants Argentina to take their form into next year's World Cup in Qatar, when he will be 35.
"When you win, you have to take advantage of that momentum," he said. "It's easier when results accompany you. We must take advantage of this [win] and this selection of players.
"I told them they're the national team of the future, and I was not wrong. They proved it by winning this Copa. We've been working together for a while now. It's a great group of guys. I am happy to be part of this group."
After a long season, Messi will have some time off with his future at club level unresolved. Barca president Joan Laporta has said Messi wants to sign a new deal, but the club's financial problems are holding up registering a potential new deal with La Liga.