He also recalls the empathy he had for Bernhard Langer, who missed the slithery 6-footer on No. 18 that gave the Americans the victory.
In the aftermath of cheers, O'Meara thought of his European rival and was 'sad for him because you wouldn't want anybody to be in that position,' he said Wednesday.
O'Meara, Hale Irwin, Raymond Floyd and other competitors from those famed Cup matches return to The Ocean Course this week for the Senior PGA Championship.
Langer's putt ended three days of agonizing, compelling drama, where many of the world's best players were sent to their knees by Pete Dye's fearsome layout.
'I remember the horror stories we saw there,' said O'Meara, the former Masters and British Open champion playing his first Senior major.
O'Meara stood around the 18th green with his U.S. teammates and captain Dave Stockton -- who'll also tee it up this week -- to watch Sunday's final singles match between Langer and Irwin.
With the United States ahead 14-13, Langer needed to win the final hole to win his match and force a tie which would have sent the cup back overseas. Instead, Langer missed his par putt.
Irwin was already in with a 5 on the 18th when Langer's turn came. At some of the practice rounds, Irwin noticed the grain on the green seemed stronger back to front than on other greens. He urged his teammates to remember that when they came to the last hole.
'Was I hoping he would make it? Of course not,' said Irwin, a four-time Senior PGA winner. 'There was little I could do about it. But I was wondering if (Langer) knew what I thought I knew. And he did not.'
There was no need to worry about Langer, though. Both O'Meara and Irwin praised his mettle in winning a tournament in Germany the following week.
The Ocean Course has not hosted such a high-profile event since. It held the World Cup in 1997 and 2003, and the first Warburg Cup match-play competition -- in which Langer took part -- six years ago.
While Dye and his crew subtly tweaked the course the past 16 years, the Atlantic's swirling winds ultimately will decide if this week's event is remembered in the same somewhat fearful way as that long-ago Ryder Cup.
Irwin chuckled as seaside gusts rattled the tent as he spoke. The wind is forecast at up to 25 mph, strong enough to send any preparation from Tuesday's pro-am 'halfway out the window,' Irwin said.
If the breezes blow even harder Thursday, anything you've done in practice is gone 'and it's dragging behind you in the car,' he said.
Depending on the wind's direction, O'Meara said, you could hit driver, 4-iron to reach the par-4, 394-yard first hole one day and then use 3-wood, sand wedge a round later.
'To me, that's kind of what golf's all about, to have change of the elements depict how a golf course is going to play,' he said.
Defending Senior PGA champion Jay Haas thinks the ocean breezes could mean the winner finishes over par. Then again, he heard the same warnings at last year's event at Oak Tree Golf Club.
'We played some practice in some pretty heavy winds there and that was the so-called toughest course in America when it was built and all that,' Haas said. 'So I think there were some guys, myself included, having nightmares about the course.'
Instead, Haas won the first major of his career at 5 under par.
Irwin, perhaps carrying the memories from 16 years earlier, is wary of what's ahead. The Ocean Course, he said, 'could manufacture some scores that will be unbelievably high.'
Those earlier competitions, Irwin noted, were match play. This competition is vastly different.
'In match play, you're out there slashing away and you can give it up and only lose one hole,' he said. 'But out here you slash away and you can lose your life.'