Carter coached Federer throughout his formative years until he died while on honeymoon in 2002.
Zverev won the biggest crown of his career when he overpowered Novak Djokovic at the ATP Finals previous year, but questions remain over whether this new kid on the block can dismantle the dominance of the big four - Djokovic, Roger Federer, Rafael Nadal and Andy Murray.
Federer will be out to win Grand Slam No 20 but will face a battle to do so with Novak Djokovic, Rafael Nadal and Andy Murray all set to compete. Speaking emotionally, Federer said: "I miss him so much, I hope he would be proud".
Although the 6-4, 6-2 win over Zverev in the Hopman final reversed a loss to the German in London in November, Federer said he was just one of many challengers in Melbourne. I guess it was somewhat of a wake-up call for me when he passed away.
Federer added: "So Peter was a really important person in my life and if I can say thank you today for my technique, it's to Peter".
"Geez, never broke down like this", he said later.
"I don't know the draw yet, I don't know who my first round opponent is, I don't know if I play on Monday or day or night".
"I've been incredibly fortunate and we had the right people at the right time, the right coaches at the right time".
When Federer learnt of his coach's death, he ran through the streets "bawling and hysterical".
"I guess he didn't want me to be a wasted talent".
"The amusing thing is we have four different formats in four Slams, so it is important to remind yourself what's going on and which one it is", said Federer.
But Federer, aiming for his third successive Australian Open title and seventh overall, said he was personally "a bit torn" between the options.
"Sure you could argue I made those decisions, but I also got lucky along the way".
Federer told The Australian in 2012: "He wasn't my first coach, but he was my real coach".
"Am I confident? I don't know".
While many would say the tennis star is a natural talent, Federer himself claimed he's had a lot of luck along the way, especially with his coaches, such as Carter. "Still happy playing and I've won the last two Australian Open editions so I should be going in there with confidence", he said.
"There's so much that connects me to that country". Worryingly, he pulled out of the Brisbane International last week with a thigh strain but then played an exhibition in Sydney and insists he will be ready for Melbourne.