And in the wake of the All Whites' heart-stopping draw with Slovakia, the always colourful Fallon has even picked out Italy's weak point.
In stark contrast to their wild celebrations on the field, Ricki Herbert's men were calm and reflective after the thrilling draw at Rustenburg.
But Fallon, a very public Christian, was in top form, even suggesting that the All Whites had divine help in netting this country's first World Cup point.
The All Whites take on Italy at Nelspruit, and Fallon, when asked if the 2006 winner could be beaten, replied "definitely".
"We can beat the best. We've got a good enough team to do that," he said.
"I personally believe we can go through to the next round.
"People think I'm mad but people didn't think we would get a point against Slovakia and it's happened. We're going to prove people wrong.
"This will make waves in New Zealand. This is a landmark and we know we can kick on and do better.
"We've watched video of Italy and they struggle on the crosses and the long diagonal ball.
"Hopefully we can get into the game through that and play good football. We showed today that we can do that and had a lot of possession.
"Italy are a brilliant team, world champions, and I'd never be so cocky to say we will beat up the champions, but we never go out thinking we are going to lose."
Fallon almost portrayed the All Whites as the Band of God, saying intervention from above had helped Winston Reid score his historic last-gasp goal against Slovakia.
Fallon said the owner of the Serengeti Estate, where the All Whites are staying, had played a part.
"Graham Power prayed for the team and even Winston said he prayed before he went to bed and he said he never believed in it... he prayed and he scored a goal. That's the power of prayer.
"I don't even think Winston realises what he's done yet. I said to him `you've made history.'"We're making history.
"It was surreal to even be out there in the World Cup. But I just know something special is happening."
When reminded that Italy is fairly renowned in the religious stakes, Fallon laughed and replied: "I know...we'll see who believes the most."
He added: "It's the phoenix.. New Zealand football has been in the ashes a long time, waiting to rise back up.
"Today we've done it. It's a team game and we play as a team."
Herbert wasn't quite as forthright, but the usually restrained coach evoked last year's shock performance against the world champions in Pretoria, when the All Whites led three times and lost only 3-4.
Herbert said: "We've got two heavyweights to go [Italy and Paraguay] and it will be tough.
I'm sure the Italians will be hoping to score three points off us and go into the Slovakian game with a bit of comfort.
"We played them before the Confederations Cup last year so we have a bit of a relationship.
"If these games are too big they are too big. But we know we have a chance like everyone else.
"They'll certainly know they've been in a football match."
Record-holding veteran Ivan Vicelich said Kiwi supporters in the Rustenburg crowd had helped inspire the players against Slovakia.
"We could hear them and we could definitely see them dressed all in white. It was great to see so many," he said.
Captain Ryan Nelsen: "I'm still being picky and not happy - we could have done a bit better.
"But in the greater scheme of things it was a case of well done."
The All Whites reported no major injuries.
The only down side was the yellow cards picked up by Tony Lochhead and Reid, for taking his shirt off in celebration of his goal from a superb Shane Smeltz cross.
A second yellow card in the group matches means an automatic suspension.
