Murray, 36, a former world no. 1, lost to 19th seed Grigor Dimitrov, 6-3, 6-4, 6-1, in New York.
Murray, who is currently ranked 37th, has not advanced past the round of 16 at a major since returning to competition in 2019.
"It's incredibly difficult to play at the highest level," he remarked.
"It's frustrating when you can't play as well as you'd like.
It's possible that the deep runs, along with everything else I thought I was capable of, simply aren't.
Despite frustrations, Murray continues to like his work.
As the three-time Grand Slam winner enters the last stages of his career, Murray's primary goal this season was to make a deep run in a major.
The Scotsman advanced to the third round at the Australian Open in January and the second round at Wimbledon last month after boycotting the French Open.
Despite these defeats at the majors, Murray has continued his ascent, reaching his highest ranking since his comeback four years ago.
I still take pleasure in all of the work that goes into it. In February, Murray made it all the way to the final in Doha, and he has already won three titles on the ATP Challenger Tour, which is the second tier of the ATP's professional circuit.
That's what motivates me to keep going.
"If I stop enjoying that - or my results, my ranking, and everything starts to go backwards, if in a few months' time I was ranked 60 in the world, or whatever, instead of moving up, then things might change."
Seeding for the four Grand Slam tournaments would theoretically increase the chances of advancing farther in the majors.
Because of an abdominal injury, the Scot had to skip events in Toronto and Cincinnati this month, setting back his hopes and dreams.
Having a seeding outside the top 32 for the US Open hurt his hopes in New York.
After overcoming his injuries, Murray defeated Corentin Moutet of France in the first round, but he struggled against Dimitrov.
Murray, who was knocked out of Wimbledon by fifth-seeded Stefanos Tsitsipas, said, "If I want to have deep runs in these tournaments, I'm going to have to come up against players like Grigor."
"Just because I'm seeded in the top 32 doesn't mean I'm guaranteed a deep run," I said.