SÃO PAULO—In the final moments of Brazil’s nail-biting win over Chile at the World Cup on Saturday, the hometown favorites looked more like a team headed for a meltdown than soccer glory.

Several players were sobbing as coaches and teammates struggled to console them, a teary scene that’s raising questions about whether the Seleção is cracking under the immense pressure of trying to win the World Cup at home.

While athletes shed tears the world over, it usually happens after the final whistle. In this case, the Brazilian players were weeping before the match had even ended.

With the team facing a must-win game against Colombia on Friday, the Seleção’s emotional state has become a national concern. “Seleção seeks emotional control,” was the headline Monday in the O Estado de S. Paulo newspaper.

The crying began when the Chile game went to a decisive round of penalty shots after remaining tied at 1-1 after 120 minutes of play. There is a heavy dose of luck in the outcomes of penalty rounds. Suddenly the exhausted Brazilians faced the real possibility of being knocked out of their own World Cup by a jinxed shot or a charmed deflection.

Players had tears running down their faces by the time the first shooters took their place in front of the ball. The captain, Paris-St. Germain defender Thiago Silva, was seated on a soccer ball crying. Paulinho, a midfielder who had been benched for poor play, knelt by Thiago Silva in an apparent effort to calm him down.

After the game Thiago Silva told reporters he was so nervous he’d asked not to be called to take one of the first penalty shots, and was relieved he didn’t have to take one in the end.

That’s because Brazil’s young star, the Barcelona attacker Neymar, put Chile away with a coolly executed penalty strike, capitalizing on Brazilian goalie Julio Cesar’s defense of two Chilean shots. Moments after Neymar scored the winning goal, the spiky-haired midfielder fell facedown on the field, his head buried in his arms and his stomach visibly heaving in convulsive sobs.

By this time, multiple players were bawling. Even the stoic defender David Luiz, who also plays with Paris-St. Germain, was red-eyed. Thiago Silva was on his knees in the belly of Brazilian Coach Felipão, who was trying to console him.

In the days since, team and country officials have sought to play down the scene as a one-time outpouring following a difficult game.

Speaking at a news conference in Rio de Janeiro on Wednesday, Neymar said the team had recovered. “There’s no emotional problem. Everybody is all right. It was an emotional game. There was some serious emotion, and each person has their own way with it.”

Brazil’s Sports Minister Aldo Rebelo said in a Wednesday interview, “It is natural that the emotion of the fans, the players, of everyone, has reached a higher level of sensibility. Crying is a natural manifestation in certain moments in people’s lives.”

It’s hard to overstate the pressure on Brazil’s national team. In a country that has won the World Cup more than any other and that sees much of its national identity in soccer, there is an enormous expectation for the hosts to triumph. Losing could mean infamy: People here still talk about the 1950 defeat to Uruguay at home as a humiliation. The Brazilians are the only team for which anything short of hoisting the golden World Cup trophy will be viewed as failure.

If that weren’t enough, this World Cup was thrust into the center of contentious political debates last year when around a million Brazilians took to the streets, making excessive spending on tournament stadiums a symbol for other complaints such as corruption and inefficient government services. Some Brazilians worry that if the Seleção falls short, protests may return.

The problem is, the national team officials may be magnifying the pressure, critics are now saying. Before the Chile game, team officials showed players a video documentary about child survivors of a 2011 mudslide tragedy that left many dead in a poor hillside slum of Rio de Janeiro, several newspapers reported.

Rodrigo Paiva, spokesman for the Brazil Soccer Federation, said he preferred not to respond to such critics and “let them keep talking while we push forward.”

Regarding the film, Mr. Paiva said it was about children that the team “met during practice, a beautiful story of triumph.”

Such a video could put players in an even more highly pressurized mind-set, where the future of these children is somehow linked to the team’s on-field success, according to Suzy Fleury, a Brazilian sports psychologist who has worked with several professional teams.

She said a better strategy would have been to focus on soccer—the part that players can control—by showing things like highlight reels. Images of child disaster survivors only reinforce the notion that the hopes of the nation are riding on the young team’s shoulders.

“The anxiety, the fear of losing, the fear of competing, it shows a lack of concentration. They aren’t in control of their emotions,” Ms. Fleury said. “The fragility shows that there needs to be an adjustment in the psychological preparation of the team.”

Of course, tears of emotion are not out of place in sports. Portugal’s

Cristiano Ronaldo,

on anyone’s list of the best players in the game, has cried unabashedly in several key moments in his career. Los Angeles Rams defensive lineman Rosey Grier put the issue under the spotlight for American fans by singing “It’s Alright to Cry” in a 1974 television performance.

Indeed, many Brazilians agree with Mr. Grier’s sentiment. “Crying is good,” was the headline of an editorial published Tuesday by Tostão, a star on Brazil’s World Cup champion 1970 team. “What saves the Seleção is the emotional involvement of the players, pushed by the fans and the pressure of playing at home,” wrote Tostão.

Indeed, the bigger problem may be that Brazil hasn’t played like a world champion. In addition to its squeaker with Chile, the Seleção couldn’t overcome a scrappy Mexican squad, settling for a scoreless tie in their first-round match. Brazil is relying heavily on Neymar’s individual brilliance and so far has failed to put together the kind of rapid passing attacks that characterize modern soccer.

Meantime, Colombia is advancing powerfully in this World Cup. Its young star James Rodríguez scored one of the tournament’s most memorable goals in a dominating 2-0 win over Uruguay to advance to Friday’s quarterfinal clash with Brazil in Fortaleza.

Brazilian play has been so spotty that analysts predict some personnel changes are in the offing. Struggling Fluminense striker Fred and Barcelona defender Daniel Alves are top of the list of those who may be benched for poor play, sportswriters here say. Brazil’s midfield play has essentially collapsed, and other tactical changes may come to reinforce it.

Paulinho, the midfielder benched earlier in the World Cup and who was calmly consoling Thiago Silva during the Chile game, may be back on the field against Colombia, these analysts say. His efforts to soothe his comrade show at least he’s got his head together.

—Paul Kiernan contributed to this article