Woodward was coach of England in 2003, the only occasion a northern hemisphere side has won the World Cup.
He said in his Mail on Sunday column after Japan's win over Ireland that it was a game that highlighted the importance of pace.
"Japan played at an extraordinary tempo, recycled the ball incredibly precisely and if any side can do that for 80 minutes it makes them nigh on unbeatable. I don't think Ireland will have experienced anything like that before and they had no answer," he said.
"That's the reason why, after the first round of matches, I make New Zealand slight favourites to win this World Cup because, of all the established teams, it is the All Blacks who consistently play at pace.
"And it's why I want to see England up their tempo. When I talk about pace I'm not just talking about speed of foot and incredible fitness – which Japan have in bucket loads – but speed of thought and the willingness to always get on the front foot. Japan weren't only playing at 1000mph they were thinking at the same speed," he said.
That quality had also shown through in their defence.
"They were remorseless, with all 15 players covering acres of ground. They hit hard and low, their exemplary technique making a mockery of those who say it's difficult to tackle legally in the modern heavyweight game.
"They were also very disciplined at the breakdown and ruck, keeping their penalty count very low and giving Ireland no respite.
"From the outset I gave Japan every chance of topping either Ireland or Scotland and already they have delivered one famous win. Who knows where this story might end?
"They have ignited a country and this is what World Cups are all about," he said.
Meanwhile, Ireland's Sunday Independent writer Brendan Fanning said: "The psychological damage from this will be significant. A fourth defeat from 11 Tests this year is hardly a historical landmark in the Irish game but losing to a Tier 2 nation is a shock to the system.
"[Joe] Schmidt will surely get another 10 points in the bag to guarantee a place in the quarterfinal, but when we though it was all about the Boks, now the All Blacks are back in the frame," he said.