Spain are in Bari for a friendly against the 2006 World Cup winners on Wednesday, a game in which the Real Madrid goalkeeper played a starring role the last time the sides met three years ago.
With the score 0-0 after extra-time, Casillas saved two penalties to help his side through to the last four at Euro 2008, laying to rest the memory of three previous quarter-final shootout exits.
"We took the pressure off ourselves, that game was a great relief," Casillas told reporters in Bari.
"From there, against Russia in the semi-finals, Spain's football changed radically and their luck as well, something which had never been with us before. It all changed from that moment."
Wednesday's match comes four days before the traditional curtain-raiser to the new season, the Spanish Super Cup where European and La Liga champions Barcelona take on King's Cup holders Real Madrid.
The first leg is at the Bernabeu on Sunday with the return at the Nou Camp next Wednesday.
Although Real defender Sergio Ramos and Barca midfielder Xavi have pulled out of the Spain squad through injury, 11 of the 21 remaining players are from the top two clubs.
"At present our minds are focused on Italy," said Casillas. "When Spain fell to Portugal [4-0] and Argentina [4-1] in friendlies last year we were criticised for not knowing how to defend our world title.
"We need to demonstrate Spain are world champions for a reason and work at 200 percent because our rivals will give their all."
