Federer went on to win his first ever Grand Slam in 2003 - a year after Carter's death.
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.
Over the course of his career Federer has racked up an impressive 20 grand slams, including a record eight Wimbledon titles, a joint-record six Australian Open titles, a record five consecutive US Open titles and one French Open title. "I was able to, you know, have coaching lessons with him". I guess it was somewhat of a wake-up call for me when he passed away.
Federer added: "Peter was really a really important person in my life because I think if I can say thank you for my technique today, it's to Peter".
‘Never broken down like this’ – Roger Federer in tears as he discusses tragic coach’s death
"Geez, never broke down like this", he said later.
"When it first happened, I believe it was in the Davis Cup in Basel when I played an awesome weekend against the Americans (in 2001) and of course when I won Wimbledon, the emotions were so, so strong".
Federer "left his hotel and ran through the streets, bawling and hysterical", the Australian newspaper reported. "He didn't want me to be a wasted talent".
But it was the manner of his win in London two months ago - dismissing Djokovic 6-4, 6-3 a day after a 7-5, 7-6 triumph over Federer - that had people believing the German had turned the corner and would be a major force in 2019.More news: With Vic Fangio, Broncos go with experience and toughness
Speaking after he easily accounted for world number four Alexander Zverev, the last player to beat him in singles in Perth back in 2017, Federer played down his chances of a third successive Australian Open title.
"It's a really nice story", Federer said.
"I mean, sure you could argue I made those decisions, but er, I also got lucky along the way".
Federer told CNN it was a career-changing moment.More news: Japan holds the world's most powerful passport for 2019
"I do get emotional watching movies sometimes but I did not know I had this happy cry as we call it in our family, not just when you are winning, but the kiddies", the Basel native said. But still I have a lot of things to improve. I've had another great year.
He has remained high atop the men's singles rankings throughout the past two years and he is one of OUR FAVORITES at the upcoming Australian Open.
"There's so much that connects me to that country".
"Melbourne will be the same I think. The legends that I admire, the coaches that I've had in Tony Roche and Peter Carter-they've been incredibly inspirational and important to me in my life".More news: Signature Series OLED TV R