The veteran American went into the final round at East Lake Golf Club two strokes off the pace and twice moved into a tie for the lead before finishing in a share of second place with world number one Rory McIlroy.
A poor swing with his approach at the par-four 17th led to the second of his three bogeys on the day and it was the one that really stung.
"I got trapped in between clubs a little bit on 17," Furyk told reporters after firing a one-under-par 69 in the season-ending event to post an eight-under total of 272, finishing three strokes off the pace.
"A six-iron was a little too much. I don't think seven-iron was enough.
"I was kind of trying to force the seven and got trapped in behind me a little bit, so not a very good swing. I was disappointed in that, but the rest of the day played really well."
Furyk made a sizzling to start to the final round, birdies on the second and third holes lifting him briefly into a three-way tie at the top with Northern Irishman McIlroy and eventual winner Billy Horschel.
He later regained a share of the lead after very nearly holing out with a delicate chip from greenside rough for eagle at the par-five 15th.
The 44-year-old, who won the most recent of his 16 titles on the PGA Tour at the 2010 Tour Championship, settled instead for a tap-in birdie but his title bid faded with the bogeys on the last two holes.
"It was a good week, a good solid day," he said. "Really it was nice to get off to that fast start.
"Kind of mellowed through the middle of round and started hitting some good shots. I felt like I played well."
Furyk recorded 11 top-10s in 21 starts on the 2013-14 PGA Tour, including second placings at the Wells Fargo Championship, Players Championship, Canadian Open and Tour Championship.
Asked how much his fourth runner-up finish of the year had hurt, Furyk replied: "Canada probably was the worst because I was in control of the tournament. Starting Sunday I was in control of the tournament all day and got chased down."
"The other three seconds, you know, were good efforts," he added. "I shot 65, 66 on Sunday at Wells Fargo and the Players.
"This one, Billy was out ahead. I was trying to chase him down all day. I just couldn't make enough birdies."
(Editing by Nick Mulvenney)
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