Tiger Woods will next play at the AT&T National in two weeks in Bethesda. (ROBERT GALBRAITH/REUTERS)

When Tiger Woods sent his first tee shot down the opening fairway Sunday afternoon at Olympic Club, the possibility still existed that he might come from behind and win his fourth U.S. Open championship. Even after he bogeyed No. 1, there was so much golf ahead, he could have contended.

But what followed was a miserable stretch that took Woods right out of the tournament, an event in which he shared the lead at the midway point. He bogeyed the second. He double bogeyed the third. He played the first six holes in 6 over par to get to 10 over for the tournament, and though he steadied himself, he never contended. After opening with rounds of 69 and 70, he shot 75 and 73 on the weekend — his second-worst performance, in relation to par, in the final two rounds of a major. He finished 7 over, tied for 21st.

“The first six, I just didn’t play well at all,” Woods said. “I just could never get anything going positively and I missed the ball in the wrong side a couple times, and that’s all it takes.”

Woods will next play in two weeks at the AT&T National at Congressional Country Club in Bethesda, the event which benefits his foundation. He won that event in 2009, the last time it was played at Congressional. He said his experience here, where he could have won his 15th major, gives him confidence going forward.

“I’m excited about the consistency of it, how well I hit the ball all week, really,” Woods said. “I didn’t really miss it that badly this week. The misses were just a fraction off, which is great.”

Woods’s fate Sunday didn’t come close to matching that of Phil Mickelson, golf’s second-biggest attraction and Woods’s playing partner in the first two rounds. Mickelson, five times a U.S. Open runner-up, made eight bogeys and not a single birdie in shooting a closing 78 Sunday. He finished 16 over for the tournament.

Amateur finishes

Beau Hossler, the 17-year-old high school student from Southern California who began the day only four shots out of the lead, shot a 76 on Sunday, and lost the lowest amateur honors to Jordan Spieth, who plays at Texas, where Hossler is committed to play after he graduates from high school in 2013.

Patrick Cantlay, a 20-year-old sophomore at UCLA, closed his Open with a 72 and finished 11 over, but he declined to say whether he will turn pro — as some in the industry expect — immediately after the Open.

“I haven’t made a decision yet,” he said. “I still have a lot to talk over with my family and everything.”

A year ago, Cantlay contended at the Travelers Championship in Hartford, where he shot a course-record 60, and also played in the AT&T National. . . .

David Toms, who was tied with Woods and Jim Furyk for the lead after 36 holes, closed with a 68 to finish at 3 over. John Peterson, a fellow LSU grad who counts Toms as his mentor, shot 70 on Sunday and tied Toms at 3 over.