HEARTBREAK: A fan emotes after Mexico was bounced from the World Cup by two late Dutch goals Sunday. It is Mexico’s sixth straight Cup exit after the first knockout-round game.
European Pressphoto Agency

Fortaleza, Brazil

Twice in Sunday’s pair of World Cup games, when the clock ticked to 87 minutes, teams from the Americas felt they were in touching distance of the quarterfinals. Mexico was beating the Netherlands, the hottest team at the tournament. Costa Rica was beating Greece, despite being down to 10 men.

Then came the heartbreak. Four hours apart, the sides from the Americas conceded late equalizers. What could have been a banner day for Concacaf, the soccer confederation for North and Central America and the Caribbean, was melting in the Brazilian heat.

Michael Umaña scored the winning penalty in Costa Rica’s shootout win over Greece.
Jason Cairnduff/Zuma Press

Now this is where the stories diverge. Mexico fell apart so completely that El Tri conceded a late penalty, after Wesley Sneijder’s tying goal, and lost 2-1 to the Dutch here in Fortaleza. But Costa Rica gave Concacaf’s day had a happy ending at the Arena Pernambuco in Recife. Los Ticos had to sweat through extra time, but five perfect penalty kicks in the shootout, combined with the left hand of goalkeeper Keylor Navas, lifted them over Greece and into the quarterfinals.

So the possibility of the first ever all-Concacaf semifinal is alive—although only faintly. Costa Rica now faces the Netherlands in the quarters on Saturday in Salvador. And the U.S. is still a long way from thinking about the semis—it has a difficult round-of-16 matchup on Tuesday against Belgium.

Except, wasn’t this supposed to be the other way around? Costa Rica was the knockout-round newbie. Mexico is the team that has been here before. In fact, Mexico has reached the round of 16 at every World Cup since 1994.

The last Concacaf team to make it to a quarterfinal was the U.S. in 2002, which beat Mexico to get there and eventually lost to Germany. The U.S. is also the only Concacaf nation to reach a semifinal. That high-water mark came in the fly-by-night operation that was the 1930 World Cup.

In its first attempt, Costa Rica managed what El Tri hasn’t in 28 years. Mexico is a specialist in second-round defeats, an unfortunate feat it has managed now in six consecutive World Cups.

Francisco Javier Rodríguez and Mexico weren’t so fortunate, losing to the Netherlands, 2-1.
European Pressphoto Agency

“We’ve achieved some very good things, but nobody can take away the bitter taste of this defeat,” Mexico coach Miguel Herrera said.

A minute-by-minute statistical breakdown of how the match of the day played out: Inside the Box.

In its run of six, this elimination stung the most. Mexico had led since Giovani Dos Santos’s goal in the 48th minute and tried to sit back. It can have few complaints over Sneijder’s equalizing goal—the result of a poor clearance after a Dutch corner kick—but the debate over the last-minute penalty that sent El Tri home will rage long after the team boards its flight.

Winger Arjen Robben, who had seen a more legitimate penalty appeal turned down in the first half, was typically theatrical as he flailed all four limbs, deep into stoppage time. But that masked the more important point: Replays show that Mexico’s captain, Rafa Marquez, made contact, however minor, with his foot on a tackle.

“We will leave [Monday] or the day after, but that referee will also go home,” Herrera said, speculating that the call would cost referee Pedro Proenca of Portugal another World Cup assignment.

Costa Rica was on the wrong end of a controversial penalty decision, too, though this time it wasn’t awarded.

With Costa Rica leading 1-0 through

Bryan Ruiz’s

52nd-minute effort, a Greek defender appeared to handle the ball inside the box. The referee didn’t see it. And, moments later, he made things harder for the Central Americans. Defender Oscar Duarte was sent off with a second yellow card, leaving them to defend the lead with 10 men for more than a half-hour.

But like Mexico, Los Ticos were undone in stoppage time. Sokratis Papastathopoulos tied things up, and earned the distinction of being the longest-named goal scorer in World Cup history in the process.

Costa Rica—which not only survived a group that included England, Italy and Uruguay, but finished top—wasn’t done yet. Running on fumes, it hung on through the 30 minutes of extra time. The side even survived a 5-on-2 break by the Greeks. And when it came to penalties—the second session of the round after Brazil eked by Chile on Saturday—Navas was decisive.

While his teammates watched from the halfway line, arms linked and on their knees, he made the only stop of the shootout. “Saving the penalty is one of the most wonderful things of my whole life,” he told reporters afterward.

Mexico’s adventure ended where it always does, but Costa Rica’s continues long after it was expected to be over.

Write to Joshua Robinson at joshua.robinson@wsj.com