Federer lost 6-3 5-7 6-7 6-7 to the unheralded Australian in what was one of the most surprising upsets in the tournament's history.
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The Swiss superstar refused to cite any fitness or injury problems, but did say that he struggled to breathe in the heat and humidity of New York.
Everything feels off when you’re hot. It's just one of those nights where I guess I felt I couldn't get air. One of the first times it's happened to me.
"At some point also I was just happy that the match was over, I guess. Some days it's just not the day where the body can cope with it."
Millman, unseeded and ranked 55th in the world, sealed the win in three hours and 34 minutes.
"I felt like a deer in the headlights to begin with, to be honest," he said.
"I've got to control the controllable and the one thing I can control is the fight in me. I've always brought the fight up."
Second seed Federer, who had not dropped a set in his first three matches in New York, had 77 unforced errors and 10 double faults and landed just 49 per cent of his first serves.
"I'm probably in a little bit of disbelief. I have so much respect for Roger and everything he's done for the game," Millman added. "He's a hero of mine. Today he was not at his best but I'll take it."
Next up for the Australian is a quarter-final match-up against sixth seed Novak Djokovic.