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.
The 37-year-old is in hot form having helped Switzerland win the Hopman Cup in Perth, getting 2019 off to a flawless start having won his very first opportunity for silverware in the new season.
The Australian newspaper reported he left his hotel and "ran through the streets, bawling and hysterical".
Federer learned of Carter's death while competing at the Canadian Masters in Toronto and according to 'The Roger Federer Story: Quest for Perfection, ' the book penned by Swiss tennis journalist Rene Stauffer, "he was never so upset in his life".
"I guess he didn't want me to be a wasted talent", Federer said while choking back tears.
Carter was a close friend of world No. 1 Simona Halep's former coach Darren Cahill, who was coaching Lleyton Hewitt at the same time.
"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. "We played each other at 14, 16, 20 years old, and who knew we'd be Wimbledon champions and world number ones".
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".
Unfortunately, one year before Federer was to win Wimbledon on 2003, Carter was to die in a vehicle accident whilst on honeymoon in South Africa. His eyes watered and reddened, he looked down, and said "sorry".
While a third said: "One of many reasons why I love this guy, those emotions make him so very special to show them so openly you can't help but cry with him".
"I guess it was somewhat of a wake-up call for me when he passed away, and I really started to train hard". I think what I would like to say is that I've been incredibly fortunate to have the right people at the right time, the right coaches.
"Sure you could argue I made those decisions, but I also got lucky along the way". "I feel good... I've been training really well". I've had another great year. 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. "I was able to have coaching lessons with him, and he was from Adelaide in Australia".