"I know it's going to sting for a little bit here, but given where I was to where I am now, (I feel) blessed".
He could not recover his challenge after that, and a fourth British Open title will have to wait.
For four-time major victor Rory McIlroy, who finished tied for second, two shots off Molinari, it is a different Woods to the years of his pomp. Molinari didn't make a bogey on his way to a 69 while playing alongside Woods.
Molinari finished at 8-under 276, the lowest score in eight Opens at Carnoustie, the course where Jean Van de Velde threw away the British Open with a triple bogey on the last hole in 1999, where Padraig Harrington twice hit into Barry Burn on the last hole to make double bogey and still won.
"To go the weekend bogey-free, it's unthinkable. I've watched this through the PGA Tour this year day in and day out, seeing him work as hard as anyone else". His grin grew very big as he said, "Oh, yeah". That would stem from Nos.
But despite leading the field in driving accuracy heading into the final round, he could not find the burned-out short grass at the 11th and 12th holes, and it cost him dearly. He sent his second shot into the gallery, with the ball rebounding out into the rough.
"Even though he's won 14, you have to learn how to get back", said McIlroy whose last major was in 2014.
His anger over his mistakes was tempered by perspective, comparing it to Serena Williams losing in the finals at Wimbledon. Kevin Chappell had a putt to tie the lead with Molinari at No. 16 before making double bogey on the next.
"I didn't get off to a great start, but I hung in there and I battled back", McIlroy said.
Molinari took the lead for the first time with a two-putt birdie on the par-5 14th. Tiger being back in the mix.
"I've made a lot of progress over the year that's been kind of an off year, a building year", said Spieth, who came third at the Masters in April but then missed the cut at the US Open. "Today was a day that I had a great opportunity".
Spieth also did not win, but the defending champion and three-time major champion said, "I feel fine".
The name "Woods" atop the board?
"That putt on the last, I'll never forget", he said. I thought 9 [under] would be the number.
Double bogey. Tournament lead gone, never to return. He started the round exactly how he needed to, with three pars followed by birdies at 4 and 6 to get to seven under.
"You knew you'd have three, four good looks at birdies, and the rest of the holes, you were just going to try to position it to make par". He birdied Nos. 14 and 18, the latter after an approach shot worthy of violins. But it was the American's playing partner Molinari who wrote his own script to claim his major breakthrough at the 36th time of asking. In fact, he'd won a couple of times, and none of other players to trade at less than [2.6] yesterday - Spieth, Woods and Schauffele - had won this season.