Evans was hoping to match last year's run at Flushing Meadows when he reached the last 16 but he fell to a 7-6 (11) 6-7 (3) 6-2 7-5 defeat on Court 17 after almost four hours.
The British number two missed three set points in the first-set tie-break but it was Cilic's serving, including 26 aces, that ultimately proved the difference.
"I've played some good tennis but it's frustrating that I played a guy who's very good here, he's won the tournament and he played like he probably was then, and he definitely served like it," said Evans. "That's heavyweight versus a lightweight on serve.
"It was a tough match. I just couldn't get ahead in the fourth. I missed some chances in the first and you never know what happens when you win the first but I did well to get back into the match.
"I thought Marin played probably a bit better than me. He served very well when he needed to and it was difficult to put any pressure on. I had a small chance but I'm hanging onto threads really.
"Too good from him, that's it really. I have to move on. I don't have any bad feelings about the match. My level's there, physically I was there, so it's positive."
The pair had met once before, at the Australian Open back in 2017, when Evans won in four sets and went on to reach the fourth round of a slam for the first time.
It is now eight years since Cilic won the title here, and he is in the latter stages of his career, but he has been in good form this season, particularly in a run to the semi-finals of the French Open.
The match was disrupted early on by a spectator who heckled first Cilic and then, when Evans confronted him, the British player. Evans complained to the umpire, leading to a chant of 'Kick him out' from other spectators before the man left.
"He was just ruining everybody's day really," said Evans. "Obviously he'd probably drunk a bit too much and it was better he left for everybody on the court really, there were young kids around and he wasn't using great language and not great gestures."
Evans saved two set points to send the opener to a tie-break but could not capitalise on a 6-4 lead before double faulting on his third opportunity.
Cilic, his repetitive ball bouncing pre-serve frequently reaching double figures, was showing nerves too, but on his fifth chance he finally clinched a set that lasted an hour and 22 minutes.
Evans fought hard in the second, breaking Cilic back when he served for it at 6-5 and then coming out on top of another tie-break.
After Cilic dominated the third, Evans saved a match point brilliantly at 4-5 in the fourth with a backhand down the line but three more arrived in his next service game and this time Cilic was not to be denied.
Evans will now turn his attention to the Davis Cup and Britain's campaign in Glasgow later this month.