"In hindsight, I probably shouldn't have competed at The Players, but it's a big event, and I wanted to be there to support the tour," Woods said.
"I've got to learn from what I did there and do it right this time and not come back until I'm ready."
Next week's British Open will be played at Royal St George's in Sandwich, southern England.
"I know how disappointed Tiger is not to be able to play in The Open this year," Peter Dawson, chief executive of the R&A, said in a statement.
"Naturally, we are sorry that a player of his calibre isn't able to join us at Royal St George's, but we wish him well in his recovery and hope to see him back soon, competing in front of the fans that love to see him play the game."
Leading European golfer Ian Poulter wondered whether Woods should miss the rest of the season.
"He has been so good for golf that I think everybody would like to see him fit, healthy and where he can just play with no injuries," he told reporters.
"If that means he has to take the rest of the year off, if that were me, I would be taking the rest of the year off. I don't think he should pressure himself and I am sure he won't. He will come back when he's ready."
Woods, who needs four more major titles to match the record of 18 held by Jack Nicklaus, has not won a major since the 2008 U.S. Open nor any tournament worldwide since 2009.
Apart from his injury woes, he has also been trying to rebuild his golf swing and his private life after the breakup of his marriage.
The American has won the British Open three times, in 2000, 2005 and 2006, and the only time he has missed the event since making his debut in 1995 was in 2008 when he was injured.
"I think my best years are still ahead of me," said the 35-year-old. "I'm very confident and optimistic about the future." (Reuters)