Zverev, 21, won fair and square 7-5 7-6(5) to claim a third victory in six meetings with Federer, but the semi-final ended in uproar after a controversial second-set tiebreak.
Federer was leading 4-3 when Zverev stopped mid-rally after a ball slipped from a ball boys' hand and into his line of vision. When the point was replayed Zverev served an ace.
A few points later Zverev finished off the 37-year-old with a nerveless volley, but his on-court interview was drowned out by a cacophony of boos and heckling from fans who believed the German had gained an unfair advantage.
"Look, I understand the frustration. It's just unfortunate circumstances," 20-time Grand Slam champion Federer told reporters. "Booing, I never like it. We see it in other sports all the time, but in tennis it's rare.
"So when it happens, it gets very personal and we take it very direct. I think it's unfortunate that this happened. Sascha doesn't deserve it.
"He apologised to me at the net. I was like, 'buddy, shut up! You don't need to apologise to me here. Congratulations on a great match and a great tournament so far.'
"He didn't do anything about it. He just called it how it was. He felt it affected play. There is a rule that if something like this happens, obviously you replay points."
Federer, who was already being penciled in for a Sunday showdown with great rival Novak Djokovic, said he had asked the ball boy whether or not he had dropped the ball.
"He said, 'Yes, I did drop the ball.' From that standpoint, it's okay, no problem, that happens. It's all good. I hope he doesn't have a sleepless night. It's not a big deal at the end of the day. This is life, this is sport. Definitely not mad at him. It's all good," he added.
Zverev, the first German to reach the final of the prestigious season-ender since Boris Becker in 1996, said the boos from the Fed-Heads in the crowd had shaken him up.
"I was a little bit sad at the end with the booing and reaction of the crowd," he said.
"I was very emotional afterwards. The booing went into cheering kind of afterwards, which kind of helped me.
"I was really upset afterwards in the locker room, I'm not going to lie. I had to take a few minutes for myself.
"But, you know, I hope the crowd and the people who were booing maybe look at what actually happened, maybe just realise that I've maybe not done anything wrong."