Argentines begged Lionel Messi on Monday not to quit the national team after its traumatic Copa America defeat, but his friends said the country has mistreated its greatest footballing asset.

The Barcelona superstar left the field in tears after missing a spot-kick in the Copa America Centenario final shootout against Chile on Sunday. He promptly told reporters he was quitting.

"Don't go, Leo," and "Messi, stay," fans wailed via hashtags on Twitter.

"I've done all I can, I've been in four finals and it hurts not to be a champion," Messi said.

"It's a hard moment for me and the team, and it's difficult to say, but it's over with the Argentina team."

He and the squad were scheduled to land in Buenos Aires on Monday evening after the tournament in the United States.

He is widely rated the best player in the world, but people close to Messi complained of how harshly he has been judged in his homeland.

"This lad is just saturated with criticism and being so badly treated," said Ernesto Vecchio, who was Messi's first coach in his native city of Rosario.

"He has every right to quit," Vecchio, who now runs the Messi Foundation football school for underprivileged children, told AFP.

"I don't want him to quit but when I put myself in his shoes it seems unfair that they should look to him as the savior when there are 11 players in the team."

Messi's cool head on the pitch makes him an efficient goalscorer, but his reserved manner has sometimes drawn criticism.

Ahead of this month's Copa, Messi was accused of having "no personality" by no less a figure than Argentina's own fiery World Cup-winner Diego Maradona.

Though fans may debate which is the greater player, Maradona led Argentina to World Cup triumph in 1986.

In that respect the comparison has always been unfavorable to Messi, despite him being named FIFA World Player of the Year five times.

"I knew him when he was a kid. He is very sensitive though his face doesn't always show it," said Enrique Dominguez, who coached Messi as a child at Newell Old Boys football club.

"He missed a penalty and all the wonderful things we have seen him do were ruined."

The star's departure could herald a broader change in the Argentina line-up.

Manchester City star Sergio Aguero warned that other players could also quit the national side.

"We were all devastated in the dressing room, particularly Leo, I'd never seen him in such a state," he said.

"Several players are wondering whether to continue. It's our toughest defeat to take."

Aguero did not say whether he would follow Messi in quitting but his name and those of Javier Mascherano and Gonzalo Higuain were mentioned in media reports.

Messi's Barcelona teammate Gerard Pique said he would recover from this latest international heartache.

"I know how competitive he is and he will get over it as he has many times before," the Spain defender said.

Messi's announcement followed Argentina's third loss in a major final in three years.

They were beaten 1-0 by Germany in the final of the 2014 World Cup and lost on penalties, also to Chile, in the 2015 Copa America final.

Messi also tasted defeat with Argentina in the final of the 2007 Copa America.

Messi left Argentina as a boy to train in Spain at Barcelona's youth academy. But he resisted the possibility of playing for his adopted land.

His decision to quit came after a grueling season disrupted by injury last year. He is also on trial for tax fraud in Spain.

Although he was injured for his team's opening group game against Chile, he came on as a substitute in a 5-0 hammering of Panama to score a hat-trick in 19 minutes.

In the semi-final win over the United States, he became Argentina's top international scorer of all time with his 55th goal.

After Sunday's final, his typical composure gave way to tears of frustration.

His departure left many fans no longer thinking about losing the Copa -- such as Juan Armando Menutti, 60, in Buenos Aires.

"I am more sad about him quitting," he said.

"Losing a final is something that happens in sport," wrote another fan, Fede Ruiz, on Twitter.

"But losing you is the most painful defeat of all."