Slovakia's win put them through to the second round as Group F runners-up to Paraguay who drew 0-0 with New Zealand. Italy finished bottom of the section with just two points.
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"I take all responsibility, all responsibility for what happened," said Italy coach Marcello Lippi.
"If a team turns up at such an important game like tonight with terror in their heart and their legs and is unable to express its ability it's because the coach didn't train the team as he should."
Slovakia's overjoyed goalscorer Vittek told a news conference: "It's a huge success. We've moved the limits of Slovak football. We couldn't have dreamt about this."
"Of course, we didn't expect such domination. We were better during the match. We played with our hearts and that's what decided the match today," he added.
The Azzurri drew 1-1 with Paraguay and New Zealand in earlier lacklustre displays and more sloppiness led to Slovakia's opener.
Daniele De Rossi gave the ball away and Slovakia attacked straight at the heart of Italy's wide open defence. Juraj Kucka played the ball through for a falling Vittek to score from the edge of the box beyond the reach of keeper Federico Marchetti.
The amazing defeat brought an abrupt end to Lippi's time as Italy coach and the international careers of captain Fabio Cannavaro and midfielder Gennaro Gattuso after the trio said this would be their last tournament with the national side.
Italy's best chance in the first half came when Slovakia's Martin Skrtel headed narrowly over his own bar, a mark of how poor Italy have been in South Africa, while
