"Happy with how I played today and happy how the whole tournament went from start to finish, from the first match to the last point I felt in control," Zverev told Tennis Channel.
"Every single match I thought I played well."
The German, now with nine career victories, became the tournament's first repeat champion since Argentine Juan Martin del Potro in 2008-09.
With the 21-year-old going up against fellow youngester Minaur, 19, Zverev told the crowd: "This final could be the final of the next 15 years , so I hope you guys all enjoyed it.
Asked how much better he is now, Zverev replied: "Definitely stronger physically. In general I’m a better tennis player."
De Minaur added: "He really deserved it and played too good today."
Obviously struggling from fatigue, the Australian dropped the opening four games of the first set but fought back in second.
De Minaur drew the crowd's applause when he hit a winner to hold for 3-4, after saving three break points to avoid a double-break deficit.
He saved two match points on his own serve at 3-5 but Zverev clinched the victory when de Minaur hit a backhand into the net in the next game.
Although beaten, de Minaur, once ranked 208 in the world, will soar into the top 50 for the first time when the new rankings are released on Monday, rising 27 spots to number 45.
Zverev will have little time to relax as he plays in next week's Rogers Cup in Toronto where he is the defending champion although he has a bye into the second round.
(Reporting by Gene Cherry in Raleigh, North Carolina; additional reporting by Andrew Both; editing by Clare Fallon)
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