Pundits in Italy believe Marcello Lippi's team, dull in qualifying and with several players out-of-form, have no chance of successfully defending their title in South Africa.
But Pepe, who has just joined Juventus from Udinese, points out the Azzurri were not well-backed to win in 2006 either.
"Italy are never favourites. There is a lot of scepticism from the journalists but not from the group with Lippi," Pepe boldly declared to Reuters.
"We are convinced we can do well and we will show it."
Italy open their Group F campaign against Paraguay in Cape Town on Monday before facing New Zealand and Slovakia.
Coach Lippi said versatility was his overriding concern when picking his World Cup squad and Pepe fits the bill perfectly.
The 26-year-old can play anywhere apart from defence and in goal, but his infectious enthusiasm means he would probably don some gloves if asked.
The world champions have tinkered with various systems in the build-up with a 4-2-3-1 set to be employed against Paraguay.
Pepe had looked an unlikely starter for Monday but played on the right from the beginning in Friday's final friendly against a South African league representative side and scored twice in the 6-0 win.
While pushing for a start, he also knows he is one of the first substitutes Lippi turns to given his flexibility.
"This is important, I am versatile as I can play in midfield on the wing or in attack, it's good for me but it's up to the boss," Pepe said, his head bobbing up and down with excitement before his first major championship.
Udinese survived relegation from the Italian top-flight last season largely because of Pepe and team mate Antonio Di Natale, who just could not stop scoring.
The 32-year-old striker was not a regular Italy starter during qualification but recent training sessions suggest Serie A's top scorer last term has forced his way into Lippi's team.
Little talked about in the wider footballing world, Pepe thinks Di Natale can fire Italy towards further success.
"He has had a fantastic season, he's scored 29 goals so even the numbers speak for him," the shaven-headed Pepe said.
"Let's hope that he continues like this during the World Cup because it would be great for Italy."
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