But France almost turned the dream into a nightmare, pushing Dagg and company closer than anyone could realistically have imagined before conceding an 8-7 defeat at Eden Park.
"It's pretty awesome to win a World Cup at home," said full-back Dagg, as preparations began for three days of public celebrations with the squad in Auckland, Christchurch and Wellington.
"It is a great relief. We were under a lot pressure, but that comes with being at home in the World Cup.
"I am just proud to be a Kiwi at the moment. To get that win for New Zealand, for the team, for everyone, - it's awesome."
All Blacks captain captain Richie McCaw hailed his team's courage and desire during the closest and lowest-scoring final in World Cup history.
Relief was etched deep into the faces of McCaw, All Blacks supremo Graham Henry and his coaching colleagues Steve Hansen and Wayne Smith after victory was secured by two unlikely heroes - prop Tony Woodcock and substitute Stephen Donald.
Woodcock scored the All Blacks' try, while new Bath signing Donald's second-half penalty tilted the contest. Two weeks earlier he had been whitebait fishing on the Waikato River when he was summoned as squad replacement for injured Colin Slade.
"It wasn't very pretty, but it came down to how much desire, how much courage the boys had," McCaw said.
"A lot of guys have put a lot of effort in for a long time, and they weren't going to let the opportunity go.
"You have got to keep the belief and trust. We had to dig pretty deep, but the last thing we wanted to do was panic. We managed to hang in there."
An emotional Henry will now step down as All Blacks chief - Hansen is favourite to take over - and he paid a glowing tribute to his players and support staff who made the country's first World Cup triumph since 1987 possible.
"Personally, you've got some peace, and that's a great feeling," Henry said. "This thing was about winning, and the guys have won the World Cup. That is outstanding.
"We have been through a lot together. A lot of the guys played in the last World Cup and fell at the quarter-final (against France), and to win this - there are no words for it, quite frankly."
For France, though, there was no consolation apart from the knowledge they belied miserable pre-final form to threaten an epic upset, especially after their captain Thierry Dusautoir scored an early second-half try.
"We can hold our heads high at the end of this World Cup," Les Bleus flanker Julien Bonnaire said.
"We gave it our all, just as we said we would. Unfortunately, something was missing. It's a pity."
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