New Zealand captain Richie McCaw said the feeling was "hard to describe" after the All Blacks ended a 24-year wait to win the World Cup.
The hosts edged to an 8-7 win against France in Auckland to become world champions for the second time.
"The guys dug as deep as they've ever dug before, I'm just so proud of everyone," he said.
"We couldn't have been under more pressure but we stuck to our guns and got there in the end."
The All Blacks went into the match as strong favourites against a France side who had reached the final despite being well below their best during the tournament.
When New Zealand took an early lead through Tony Woodcock's try, it looked as though they would pull away to win convincingly.
But France produced a hugely committed performance and, after a penalty from All Blacks replacement Stephen Donald made it 8-0, Thierry Dusautoir's converted try saw them put New Zealand under huge pressure in a tension-racked final half-hour.
Donald was the fourth-choice fly-half after Dan Carter, Colin Slade and Aaron Cruden - during the first half of the final - all succumbed to injury.
"The key [to winning the tournament] was expecting things like that to happen," said McCaw. "If you hope for the best and don't prepare for it, when adversity comes you're not ready for it.
"When you lose a guy like DC [Carter] it would be easy to drop your lip. But the next guy stepped up. I take my hat off to Beaver [Donald] but it is hard to pick out one guy."
Speaking of their long wait for the title, McCaw added: "I think at some stage some team was going to do it and this group of 30 had the opportunity.
"You just have to keep getting up and believing in the mate beside you and trust in him and make sure you do your job. Everyone around New Zealand has given this team so much over the past six weeks and now we've repaid them.
"There's going to be a lot of stories told as we get older but no-one here can take it away from this group. They're tough men and I think the whole country should be very proud of every single one of them."
For New Zealand coach Graham Henry it was the final game of an eight-year reign, which included defeat by France at the quarter-final stage in 2007.
"Marvellous. The people have been have been outstanding in support of the team and the Rugby World Cup. I'm so proud to be a New Zealander standing here," he said.
"There was a bit of turmoil up there in the coaching box. Richie and the boys just hanging in there right through 80 minutes to win this thing is superb.
"This is something we've dreamed of for a while, we can rest in peace.
"I've got so much respect for what the boys have done over eight years. It's been outstanding."
Hooker Keven Mealamu described the final as "probably the toughest 80 minutes of our lives".
"We knew it wasn't going to be easy," he added. "The French really came to play tonight and it took an 80-minute effort from us."
Scrum-half Piri Weepu, who was replaced in the 49th minute after a display that saw him miss three kicks at goal, said he hoped the All Blacks' victory would relieve the burden the nation has carried since their win in the inaugural 1987 event.
"I think everyone can sleep easy now and not worry so much," he said. "I think everyone will feel a lot better now."