The Southport ace carded a stunning final round of 63 at Shinnecock Hills, agonisingly missing from eight feet for birdie on the 18th to equal the all-time major record of 62 set by Branden Grace in last year's Open Championship at Royal Birkdale.
The 27-year-old's score still matched the lowest in US Open history and set a testing clubhouse target of two over par, with Koepka the only man able to beat it - by a single shot - following a closing 68.
Fleetwood, who was fourth behind Koepka last year and partnered him in the final round at Erin Hills, said: "It's my first ever Father's Day as a father. I enjoyed that and I enjoyed watching the golf.
"As a golf fan it was good watching how he handled himself down the stretch and how he won another major. As a player who was one behind him it wasn't great to watch but you have nothing but respect for him and I enjoyed how he did it.
"That was pretty much time well spent. All in all, it's been a great day."
Koepka had played just five events before this week after missing several months of the season with a wrist injury and had to recover from being seven over par in the early stages of his second round.
"I always felt like I had a chance," the 28-year-old said. "You make a couple of birdies and you make up a lot of ground. I felt like I was never out of it; I was hitting it well, putting it well and just needed to keep grinding.
"I knew the conditions were going to ease up a little bit, and they did and I just took advantage of it. It's incredible to have my name on there (the trophy) twice and to go back-to-back is even more extraordinary. I am truly honoured.
"I did not drive it great but you can make up so much with a hot putter. The great bogey I made on 11 was big. I would have taken double bogey because we were in jail. I could easily have been derailed with a double or triple bogey."