(CNN) -- Holders Brazil were knocked out of the Copa America Sunday, after a woeful penalty shoot-out display against Paraguay in Argentina.
The star-studded Brazilians missed all four of their spot-kicks as Paraguay went on to win 2-0 and earn a place in the last four of the competition.
A disappointing match ended goal-less, as both sides finished with 10 men on the pitch after Brazilian midfielder Lucas Leiva and Uruguay's Antolin Alcaraz were dismissed following an altercation in extra time.
Brazil dominated much of the possession but lacked a cutting edge, despite fielding an attack-minded line-up led by Robinho, Alexandre Pato, and Neymar.
Neymar was particularly profligate in front of goal, twice missing golden opportunities in the first half. The first chance came on seven minutes when his volley from close range dipped over the bar; while the second saw him blaze wide on the half-hour mark, after Ganso's pass found him unmarked on the right-hand side of goal.
Paraguay goalkeeper Justo Villar was also in inspired form, showing particularly good reflexes late on to deny Milan's Pato as he raced through one-on-one.
After the match Paraguay coach Gerardo Martino admitted his side, which last won the competition in 1979, were fortunate to beat the much-fancied Brazilians.
"Brazil should probably have won it over the 90 minutes," he told reporters, in quotes carried by Agence France-Presse.
His goalkeeper Villar agreed. "It really took it out of us playing Brazil -- they dominated almost the whole match. But the team kept its shape and kept its concentration and those factors took us through."
Meanwhile Brazil's coach Mano Menezes was keen to look ahead to his team's future challenges.
"When you lose you know you made some mistakes," he told AFP. "But this happens in football and we have to live with it. The object has always been to get a strong team together for the World Cup in 2014."
The shocks continued in the second quarterfinal played Sunday as Venezuela beat Chile 2-1.
Oswaldo Vizcarrondo put Venezuela ahead on 34 minutes, but Humberto Suazo equalized for Chile midway through the second half.
Chile pushed for victory, but as extra time loomed it was Gabriel Cichero who gave Venezuela a semifinal clash with Paraguay.