The German had qualified in 11th place for his first race for the Swiss squad, but a hydraulic problems meant he could not make it to the grid in time.
Qualifying took place just six hours before the start of the race after it was postponed from Saturday due to poor weather.
Hulkenberg admitted it was especially painful not to be able to get useful mileage so early on in the season.
"I'm bitterly disappointed about what happened today, but at the same time I'm not blaming anyone," said Hulkenberg. "Things like this happen in racing.
"What is particularly bothering me is the fact that I lost all this mileage today, which is so important particularly at the beginning of the season. It would have given me a lot of valuable data and information for the next races.
"Obviously, Melbourne is not a good place for me. It was my third grand prix here and the third time that I leave this place empty handed. The only good thing is that the next race takes place next weekend."
Rookie team-mate Esteban Gutierrez finished his first Formula 1 race in 13th position.