"My first thought was was 'Geez my students have done a pretty good job on this accent'," the Australian-American astronomer said Wednesday.
"She asked me to confirm that I was Brian Schmidt and told me I had a very important call, and then the members of the panel went out and read the citation to me and congratulated me."
"I feel like when my first child was born. I'm kind of weak in the knees and a little, you know, I guess a little - hard to describe - almost speechless at this point."
Schmidt, 44, was named joint winner of the Nobel Physics Prize in Stockholm on Tuesday for his work on the 1998 discovery that dark energy - gravity's repulsive opposite - was driving an ever-increasing expansion of the universe.
Prime Minister Julia Gillard said the award was a testament to his "rigour and determination", congratulating Schmidt, US colleague Adam Riess and their competitor Saul Perlmutter, also from the US, on the joint Nobel prize.
"This discovery turned some of our most stable notions of the universe on its head and challenges our understanding of its very composition," said Gillard.
"They stuck with their observations and made the theory fit the facts, however revolutionary and inconvenient."
It was so groundbreaking Schmidt admitted having to overcome his own self-doubts about his findings, which went against the scientific orthodoxy of the time.
"It seemed too crazy to be right. We were a little scared," he told ABC Radio.
By his own admission Schmidt's research is "bleak" stuff: Earth's galactic neighbours hurtling away at unimaginable speeds to ultimately leave mankind's home in a cold, deserted Universe.
"Right now I look out into space and I see billions of galaxies. In the future I will look out and see an empty Universe," Schmidt told reporters Wednesday of his prizewinning work.
"All the galaxies we see now will be so far away that their light can no longer reach us... and our galaxy of stars will slowly fade away and die and we're left with a bunch of stellar embers and a dark universe."
It's a prospect some hundreds of billions of years in the future, but "that's not too long by astronomical standards", he added.
Schmidt was 27 when he moved to Australia in 1994, having obtained his PhD from Harvard, and said there were few other places in the world he could have done such world-class research at such a young age.
He formed the High-Z SN Search team, a group of 20 astronomers on five continents who used distant exploding stars, or supernovae, to trace the expansion of the universe back in time.
Schmidt said knowledge was a "funny thing" and while he was "pretty certain" his dark energy theory was correct "you're never absolutely certain".
It was also impossible to know where the discovery would lead, he added.
"I do not know whether the accelerated universe is going to give us a better toaster, but I do know that it will help us understand the universe, and what that eventually evolves into is to be determined," he said.
Australian Academy of Science president Suzanne Cory said it was the first time an Australian had won the Physics Nobel since 1915, declaring it an "absolutely wonderful day" for the nation's scientists.
A winemaker in his spare time, Schmidt said he was mostly looking forward to life going on as normal, starting with his weekly third-year cosmology lecture later Wednesday at the Australian National University.
He plans to put his share of the US$1.5 million prize money, to be awarded at a ceremony in Sweden in December, towards "some sort of public good" in consultation with his 20-person team.
"I like my life as it is, so I'm hoping that it doesn't change too much," he said.