Zverev, ranked number four in the world, lost in his round of 32 match against Chung Hyeon.
The 20-year-old, who is tipped for a bright future but has so far never got past the fourth round of a Grand Slam, was devastated with the defeat.
But Federer stepped in to pick up his spirits with words of encouragement to the youngster.
The Swiss star explained how he reflected on the early part of his own career to try and install confidence back into the German, who he described as “crushed”.
“I remember I had a hurdle to pass the quarters. I only did that back in 2003 for the first time,” Federer said.
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“I was 22. Either I played quarters or I lost first round.
“That’s what I told Sascha. I said, ‘Be patient about it. Don’t put yourself under unnecessary pressure. Learn from these mistakes. Whatever happened happened.’
“Unfortunately you have to believe in, how you say, the process you’re right now in. You had a good off-season.
“You’re working hard. You’re doing the right things. It’s maybe not paying off at the slam level, but just stay calm, don’t dig yourself in a hole.
“He looked crushed when I saw him. I gave him a tap on the shoulder and said, ‘C’mon, it’s not too bad. It could be worse.’”
Federer instead thinks Zverev should focus on reaching the latter stages of major tournaments rather than setting his heart on winning them from the outset.
“He’s still very young, still up-and-coming to some extent,” Federer added.
“He’s still seeking the breakthrough on the Grand Slam level.
“I just think it’s important to sometimes take a step back and actually see the good things you’ve done, give yourself time, maybe set the bar a bit lower.
“First let’s maybe try to look for a quarters or a semi-finals, not just right away think coming to the Australian Open, US Open, I have to win this thing.
“I know people talk, but for the player, it’s not easy if you’ve never been there.”