Wilkinson landed a drop-goal in the last minute of extra-time to clinch a 20-17 victory for England, as well as kicking four penalties earlier in the match, while the forwards provided the No.10 with a rock-solid platform up front.
"It was an amazing performance," said Woodward. "We're very, very lucky to have him. The whole team was great, the Dad's Army kept going. I'm very proud of the whole team. It was a great effort from all involved and Wilkinson is a key part of it."
With the result in the balance right until that thrilling final score in the 99th minute, it was an epic match – arguably the best RWC Final yet.
"I think the top two teams arrived at the Final," said Woodward. "It made for a great spectacle and I think if the conditions were a bit better we would have won easier." But he warned that England would not be content to sit on their laurels now that they have become the new world champions.
"The next game is the Six Nations," he said. "We have to keep this momentum going, we have to ensure the current success is not a blip in history."
England confounded their critics who had accused them of "boring" tactics, the Men in White flinging the ball wide on several occasions, not least in the build-up to the try scored by wing Jason Robinson.
But Woodward denied that his team's performance owed anything to a conscious switch of tactics.
"I don't think we made any changes at all tonight," said Woodward. "We played the way we have played for the last couple of years and we have proved that week in, week out. The Australian media clearly thought we were not as expansive as Australia. "We played a far more expansive game than Australia and that's a fact.
"There's been no magic plan or scheme. We've just gone game to game. England have done it the right way this time. We've gone full-strength in every match. Apart from the warm-up game in Marseilles we haven't used a Test match to not play our best team. International rugby is about today, not last week or next week."
By Justin O'Regan in Sydney