Woods thinks he'll have plenty of chances to get revenge.
McIlroy shot a 5-under 67 to beat Woods by 1 stroke in an 18-hole match between the two top-ranked golfers at the Jinsha Lake Golf Club in central China on Monday.
"This is certainly not like most Mondays. To have this many people come out and watch us play golf in an exhibition was something special. This doesn't happen," Woods said. "As far as doing something like this down the road, it would be fun."
The event, dubbed "Duel at Jinsha Lake," marked the first time the two golfers had played head-to-head without other competitors. It probably won't be the last.
Woods said he'd relish the chance to take on McIlroy more often to create a rivalry at the top of the game similar to the ones between Roger Federer, Rafael Nadal, Novak Djokovic and Andy Murray that have made men's tennis so exciting in recent years.
"If you look at the history of the game, it's not like other sports where the guys play against each other all the time. Jack (Nicklaus) and Arnold (Palmer) didn't go at it that often," Woods said. "But you know what, if we can do this for the next 10, 15 years, then certainly we can have that type of rivalry.
"I think having matches like this to promote the game of golf is what it's all about. We're trying to promote the game of golf in this region, and it's come a long way since my first time here 11 years ago."
McIlroy took an early lead with two birdies on the first three holes and held on to beat Woods, who had two bogeys to go with his six birdies for the day. The 14-time major winner finished with a 68.
Both players competed elsewhere Sunday and had to make long journeys to Zhengzhou, an industrial city in China's Henan province. McIlroy finished second to Peter Hanson in the European Tour's BMW Masters at Shanghai, while Woods tied for fourth in the PGA Tour's CIMB Classic in Malaysia.
McIlroy, who captured the PGA Championship in August for his second major, said the win over Woods offered some consolation for his defeat Sunday when he surged back from 4 shots down against Hanson only to lose by 1 stroke in the end.
"It's been a nice distraction to not dwell on what happened yesterday. I let a great chance to win a golf tournament slip through my fingers," McIlroy said. "Coming to do something like this today has definitely made it a little easier to deal with."
After falling 2 strokes behind on the front nine, Woods hit a perfect chip shot from the fairway on the par-3 12th hole that hit the pin and dropped in for birdie, bringing him within 1 shot of the Northern Irishman.
However, he then missed a long putt for par on the next hole, settling for bogey, while McIlroy sank a 7-footer for par.
Woods made birdie on the 14th hole to pull within a stroke again, but he missed his final chance to level the score on the 18th when he misplayed his approach shot and landed in a bunker, muttering, "Where did that go?"
The first head-to-head matchup between Woods and McIlroy -- at the eight-player World Golf Final in Turkey this month -- was far more one-sided. Woods shot a 7-under 64 to defeat the Northern Irishman by 6 strokes in a group match at the exhibition event.
China has lured a number of the world's top players with lucrative exhibitions in the past few years as part of an effort to grow the sport's popularity and market a bevy of new celebrity-designed courses.
No expense -- or extravagance -- was spared in welcoming Woods and McIlroy to the Jinsha Lake Golf Club.
As stunt planes buzzed overhead, a fleet of Rolls Royces whisked the players to the course, passing helicopters for sale and Aston Martins and Maseratis with showgirls draped over them. After the two struck a gong to open the event, fireworks exploded behind them and confetti cannons rained gold flakes over the jostling crowd.
Some spectators, however, were skeptical whether an event like this would actually attract new fans to the sport in China.
"The bosses here maybe want to sell the villas so they introduce two big stars to come here," said Michael Wong, vice editor-in-chief of China's Golfweek magazine in Beijing. "It's a show more than a game."
Nonetheless, fans on the course were excited to see golf's biggest names.
Ji Tianxin, a 14-year-old student and occasional golfer, came with her father from Nanjing to watch McIlroy, her favorite player.
"I don't usually get this chance to watch the best players," she said, watching the players putt on the fourth hole. "I think the two are both stars, so I really wanted to see them."
The duel even led to some sibling rivalry between a brother and sister from Beijing. Li Weiyang is a longtime fan of Woods because he appreciates his skills and finds him "charming," but his older sister Jing Sun was rooting for McIlroy.
Jing said they didn't have a wager on the match, but she thought it was a good idea.
"The bet can be who will drive back home," she said. "It's a long drive."