Koepka won his maiden PGA Championship by two shots at Bellerive Country Club in St Louis last week.
Woods headed into the last day four shots off the lead but could only narrow that deficit to two, despite a six-under final round.
The crowd were largely willing on the 42-year-old golfer, who’s looking ever more likely of reaching the levels he did before his lengthy injury lay-off.
Woods was in the third to last group to finish their final round, but it was what he did afterwards which pleasantly surprised Koepka.
Instead of going into the clubhouse, Woods waited at the 18th to congratulate the No 2-ranked golfer on his victory.
“You know that was surreal, it really was,” Koepka told Dan Patrick on The Dan Patrick Show.
“To hang around there on 18, I know he finished about 30 minutes before, but to hang around… I wasn’t expecting it.
“It was probably the coolest gesture he could have done. It was fun going toe-to-toe with him and Adam Scott, the two guys I looked up to my entire life.
“To battle it out with them, I mean, if you had told me when I was 12 years old that would have happened, that would have been a dream come true.”
Koepka, 28, has enjoyed a successful 14 months, also winning the US Open twice.
It won’t be until April 2019 that either Kopeka or Woods can get their hands on another major, however.
Speaking of his rival, Woods said: “What he’s doing is tough to beat. When he hits a 340-yard drive down the middle, that’s tough [to contend with].
“I played with him in a practice round and he was literally hitting it 340, 350 yards in the air. When a guy’s doing that straight – it’s tough to beat.”
On coming close to two majors, the 14-time major winner said: “I didn’t know how many tournaments I’d play this year, or if I’d even play. Each tournament has brought about its own challenges.
“If you’d have said at the beginning of the year that I’d have a chance to win the last two major championships… I didn’t have a swing at the time. It’s been a hell of a process this year.”
Source : EXPRESS