Greenwood is confident despite accusing England of bottling it like USPGA runner-up Jason Dufner in their warm-up defeat in Wales.
World Cup-winning centre Greenwood, who watched England blow chance after chance to kill off their opponents in Saturday's Test at the Millennium Stadium, also tuned in for the last golf major of the year to see Dufner throw away what appeared certain victory in the final few holes.
It was very much a case of deja vu for former Harlequins star Greenwood, who insisted England deserved to have their profligacy punished by Wales.
"Being a humble Englishman leaving Cardiff on Saturday night, they thoroughly deserved their victory," said the 38-year-old, speaking at Twickenham to promote the second Help for Heroes benefit match, which this year will pit the Northern Hemisphere against the Southern Hemisphere.
"For England, I don't think it's a case of throwing the baby out yet with the bathwater.
"They showed some tremendously powerful passages of play, some tremendous opportunities manufactured.
"But as Jason Dufner found out in the USPGA last night, you can drive for show but it's all about putting when it comes down to the big events, and rugby's the same.
"You can get yourself in the right position, you can find yourself with all the territory in the world, but if you can't get across the blooming white line then life becomes very difficult.
"So there are some questions that (manager) Martin Johnson still has to resolve.
"But not being one-eyed, not wearing rose-tinted spectacles, I still, still believe that this is a very, very good England side, a very powerful England side.
"And when they get the confidence to play with ball in hand 20, 25 yards out, I feel as though they are going to score.
"I think they will suddenly turn themselves into a side that no one, absolutely no one - not even New Zealand - will be comfortable about playing in a knockout stage.
"I'm very, very bullish."
Greenwood predicted a "big reaction" to Saturday's defeat when England play their final warm-up game in Ireland.
However, they have not won in Dublin since 2003's Grand Slam decider and were easily beaten trying to complete a clean sweep in March's final RBS Six Nations match.
Defeat there a week on Saturday would therefore be a third in four matches, arguably undoing all the good work of the past 12 months.
However, England went into the last World Cup in much worse shape and still managed to battle their way to the final.
That was pointed out by Jason Leonard, the world's most capped forward and Greenwood's team-mate in England's triumphant 2003 side.
"I think England can get there, as they showed in the last World Cup," said the 42-year-old.
"Everyone had written off England prior to that."
Despite his optimism, Leonard backed hosts and clear favourites New Zealand to end their recent World Cup hoodoo.
"It is theirs to lose," he said. "How they cope with that pressure is going to decide the World Cup.
"There's a heavy burden of expectation on their shoulders. They have been the best team in the world, consistently.
"I actually think they've got the players to do it."
Leonard is hoping to convince some of the stars of the tournament to take part in the upcoming 'Heroes Rugby Challenge' at Twickenham on December 3.
The fixture, which was announced today, follows the success of the same event three years ago, where 52,000 spectators helped raise £1.46million for Help for Heroes.
This year's match will see a Northern Hemisphere XV tackle a Southern Hemisphere XV, with each team containing professionals and ex-professionals as well as rugby-playing members of the armed forces.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.