The Repre captain, who plays his club football in Serie A with Napoli, was one of their key players in the 3-2 victory over the defending champions earlier this week that put them out of the competition.
Marcello Lippi's team eventually finished bottom of Group F, won by Paraguay, with even New Zealand finishing ahead of them on the standings.
Hamsik told www.cas.sk: "Few people expected the Italians to be bottom and exit so early. It is sad that they lost. Messages that have come to me from Italy, though, is that they will now root for Slovakia. This is a big failure for them, but it's football. But we are very happy now."
The Slovaks will now play Holland in the last 16 with the match scheduled to take place in Durban on Monday.
Hamsik, a product of Slovan Bratislava who has also played for Italian club Brescia, added: "They have enormous strength in attack. This is a very good team, which can hold the ball well and capitalise on any mistakes of their opponent. They attack beautifully and we will have to be very well prepared, so we will have to see on the pitch.