McKenzie then thanked his wife Hannah and his "parents for never encouraging me to get a real job".
He also thanked the late Muppets creator Jim Henson: "It's a true honour to work in the shadow of such legends."
In the press room after the ceremony, McKenzie noted New Zealand's relatively rich history of Oscar glory, including Jackson and Jane Campion.
"It's a great place to grow up, you can do whatever you want there," he told The New York Times. "Whereas I think in America, everyone is obsessed with their careers, New Zealand I think you just get to live your dreams."
Prime Minister John Key offered his congratulations to McKenzie, saying it was a great result.
McKenzie, 36, before the awards told the Herald he was "over the moon" to be nominated for an Oscar.
Man or Muppet, which was sung by Muppets writer and star Jason Segel, was his favourite song on the film, he said.
"I knew there was a chance, but I definitely wasn't sure we were going to get a nomination."
"I think it is the best musical moment in the film. It's the strongest musical moment. Everyone has had a time in their life when they've thought, 'Am I a man or a Muppet?'. I think it connects on multiple levels."
- Herald Online
The award-winning song: