Six shots behind Woods after the fog-delayed third round was finally completed at Torrey Pines on Sunday, he went on to birdie four of his next nine holes before fading after the turn on Monday.
Watney never got closer than five strokes off the lead, piling up four bogeys in strengthening winds over the last nine holes to close with a one-under-par 71.
"As a competitor, I wanted to give it to him (Woods)," 2009 champion Watney said after tying for fourth at nine-under 279, five behind Woods who also stumbled over the closing stretch.
"It was definitely a long shot, but I would have liked to get a little closer. But it was a tough day. I'm glad to be done, for sure."
Watney applauded the form shown by Woods, who won the US PGA Tour event at Torrey Pines for a record seventh time.
"I don't if anybody would have beaten him this week," he said. "He's definitely on his game. When he gets like that, you've got to play your best to compete, and unfortunately, I didn't today. But I'd love to have a shot at him sometime."
Asked to assess the state of his game after playing two events on the 2013 US Tour, Watney replied: "It's pretty good. You know, today was a bit rocky. I don't know if it was the wind or whatever it was.
"I'm close to doing some good things, and I just want to get a little closer next time. Although today was a bit disappointing, I'm looking forward to next week."
Watney, a five-times winner on the US Tour, has an impressive track record at the Farmers Insurance Open with five top-10s in nine starts, including his victory four years ago.
"I love it here," the soft-spoken 31-year-old said. "This is one of my favourite spots that we play. It's always nice to come out to somewhere where you've won."
Watney will compete in his third US Tour event of the year at this week's Phoenix Open in Scottsdale, Arizona.
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