The Swiss star was beaten by Zverev 7-5 7-6 (7-5) in the semi-finals of the ATP World Tour finals at the o2 Arena.
The bizarre incident occurred during a second-set tie-break.
Mid-rally, a ball boy accidentally dropped a ball behind Federer which seemed to put Zverev off and cause him to stop.
The umpire then decided to replay the point which resulted in Zverev serving an ace.
The German was then booed by supporters during his interview with Annabel Court after booking his place in Sunday’s final.
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After the match, Federer opened up on the incident and revealed what he said to his opponent at the net.
“I understand the [crowd’s] frustration. It’s just unfortunate circumstances. These things happen,” said Federer.
“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.
“He doesn’t deserve it. He apologised to me at the net. I was like ‘you don’t need to apologise to me here’.”
The 37-year-old then defended the ball boy, clearing up that he was not frustrated with the youngster.
“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,” he added.
“Whatever happened, this is life, this is sport. I’m definitely not mad at him.”
Federer was hoping to end the season on a high, aiming for his 100th career title.
This was his 15th semi-final from 16 appearances at the London tournament.
After the match, Zverev apologised for the incident and insisted it was not his intention to see the match engrossed into controversy.
“I apologised to Roger at the net, he told me ‘it’s okay, it’s in the rules’,” he said.
“I want to apologise to the crowd, Roger has a lot of fans here and for what he’s achieved he should have. I’m very sorry that this happened I didn’t mean to upset anybody – that’s all I can say, sorry.”