The Spaniard, one shot off the lead going into the final round, tied for fifth last Sunday after a 1-over 73.
But Garcia, the top finisher from The British Open playing this week in the Deutsche Bank Players Championship, said his 65 on Saturday made him think he might break through.
'You start getting things going right, and it seems like nothing can go wrong,' Garcia said Wednesday. 'Then it goes the other way. It's tough. You're charging pins after making a couple three putts, so you kind of go for it a bit more, and it just didn't work.'
Garcia, who has yet to win a major championship, said the British Open got away on the fifth hole, where Woods made an eagle.
'It was quite big,' Garcia said. 'He (Woods) made a good eagle there. I thought I hit a great drive, but unfortunately it just caught the edge of the bunker and was right up against the face. I couldn't even make birdie. So that was big because he goes to 15 (under), and I was stuck at 10.'
Despite the disappointing finish, Garcia remains confident.
'I felt very good last week, the best probably that I have felt all year,' he said.
Colin Montgomerie, who missed the halfway cut at the British Open, can't say the same. He withdrew Tuesday night, saying he wanted to avoid a 'competitive environment' to work on his game.
Others in the field this week include Retief Goosen, Luke Donald, Angel Cabrera, Thomas Bjorn, Todd Hamilton, John Daly, Padraig Harrington, Paul McGinley, Paul Casey, David Howell and defending champion Niklas Fasth.