Woods started the day two strokes from the lead but did not make a birdie until the ninth hole at Sedgefield.
He was three strokes behind by then and a triple-bogey at the par-four 11th totally ended his chances.
Though he bounced back with four birdies over the final six holes to shoot 70 and finish four strokes behind winner Davis Love III, the 14-times major champion was clearly disappointed.
“I had all the opportunities in the world to do it and didn’t get it done,” Woods told reporters after what nonetheless was his best result since late 2013.
“I had some makeable putts early I missed. I just wasn’t able to get any kind of roll early.”
Woods, who has not won on the PGA Tour in over two years, decided to make his Greensboro debut in a last-ditch quest to qualify for the lucrative FedExCup playoffs.
He opened with his lowest score in two years and was nearly as good the next day when he grabbed a share of the lead before slipping slightly after the third round.
Woods failed to qualify for the playoffs and said his next official event will be the 2015-16 season-opening Frys韩国半永久纹眉会所, Open in California.
He admitted on Sunday that he has a hip injury, but said it would not have prevented him from competing in the playoffs, had he qualified.
“It would have been nice, but I’m not,” he said.
Though his final round fadeout on Sunday disappointed the massive gallery, it was still a significant performance by the 39-year-old.
Major back surgery last year and some woeful performances this year, including the worst score of his career, an 85 at the Memorial tournament in June, raised legitimate questions of whether he was done as a serious threat.
His effort in Greensboro suggested more wins are in store.
But it would be premature to suggest that Woods is on track to recapturing the form of his glory days. None of the world’s top-10 players were present in Greensboro, and the course, short by modern standards, did not require him to hit driver often.
For the next few weeks, Woods will focus on his two children and his fitness.
“I got lots of soccer games to go to, so I’ll be doing that, and just working out, trying and trying to get more fit,” he said.
(Editing by Frank Pingue)