"If we do everything perfectly, at 100%, technically and tactically, we can do it," the South African, who will be replaced as coach by Perpignan boss Jacques Brunel after the tournament, told reporters.
"If we play like we did in our last two warm-ups, we certainly won't."
"The guys are in good shape," he said, adding that the side had improved in the last two of his four years in charge.
The Azzurri, who have played at every World Cup but never gone beyond the first stage, face Australia, Russia, United States and Ireland in their group in New Zealand.
The final game is expected to decide which of Ireland and Italy join group favourites Australia in the quarter-finals.
"We know it's going to be very, very tough. Even though Ireland have lost their last four warm-ups, every single one has been close," said Mallett.
Italy, whose side narrowly defeated Japan 31-24 and lost to Scotland at Murrayfield 23-12 in two test matches this month, carried off the wooden spoon once again in this year's Six Nations.
However, they showed progress by defeating France for the first time in the tournament, while narrowly losing 13-11 to Ireland on the last kick in Rome.
"They deprived England of the Grand Slam - they were fantastic and that's the Ireland we will expect to face," Mallett added.
However, Mallett, who led South Africa at the 1999 World Cup, warned against complacency in the games against Russia and USA.
"Everyone is talking about the first and last games but we've got be very careful not to mess up against Russia and the U.S. because their World Cup will be made if they beat Italy," he said.
"We need to concentrate on winning those games and go into the Ireland game with the best chance of qualifying for the quarter-finals."
"Even in our wildest dreams it will be difficult to beat Australia.
"We accept that Australia and New Zealand are the best two teams in the world but we want to gain confidence in our defence in the first phase and not lose by too many, then work hard against Russia and USA before playing Ireland."
With Stade Francais flanker Sergio Parise and Leicester Tigers prop Martin Castrogiovanni in their ranks, Italy have a strong forward line-up
But they have often lacked a cutting edge in the backline, evident in their warm-up match against Japan.
"In the Japan game, I knew they had a good backline and I risked putting my inexperienced backline in to see how it went," said Mallet.
"It didn't go very well and almost cost us the game. But.... I've got to mix and match and you have to see if the guy is up to it and if he's not up to it, improve him.
"Obviously I can't play the same 15 all the way through the tournament because that way we'd never beat Ireland. I've got to make changes and I just hope that the work we've done will pay off."