On Monday, Nagal lost 6-4, 1-6, 2-6, 4-6 in a match that lasted two hours and 30 minutes.
Nagal walked onto Arthur Ashe Stadium for his first Grand Slam main draw match without having ever earned a tour-level victory. But the 22-year-old showed little fear and won the first set 6-4 against Federer who made 19 unforced errors.
It was for the first time since 2003 that Federer had lost a set in his first-round match at the US Open.
However, in the next three sets, the world No. 190, seeking his first tour-level win, did not seem to have the weaponry to take the racquet out of the Swiss' hands and lost 1-6, 2-6, 4-6 to bow out of the competition.
Once Federer cut down his errors after the first set, he kept on top of Nagal, and recovered to enter the next round where he will face Bosnia's Damir Dzumhur.
"It was a tough first set for me. However, credit to him for playing a solid first set. I was a bit rusty in the match," Federer said after the match.
Before the match, Nagal had said he would try to enjoy the game and not think too much about whom he was playing against.
"I want to play him. It doesn't matter. It's not about winning or losing all the time. It's just the experience. It's playing someone who has 20 Grand Slams," Nagal had told ATP Tour website.
"I don't care what the commentators will be saying about me on TV. I'm going to be enjoying the crowd, playing the best tennis player ever. I'm just some dude from India. I'm fine with that until I make my name. That's it," he added.
The Indian had also said that he doesn't try to emulate Federer as the latter is just "too good".
"He's just too good. You never want to copy him. If you watch Federer and what he's doing with the ball and then you try to do the same, you're just going to break your racquets. It's never going to happen. That's why he's not my idol. Just too good. That's how I see it."
( With inputs from IANS )