"But we can tackle it calmly on the back of this good result."
"We can claim to have started this season on the right foot, immediately in the fight with the best," he said.
Vettel had hoped his achievement in securing pole position in Saturday's rescheduled qualifying session would help his quest for a fourth successive title get off to the perfect start.
But the Red Bull driver felt that tire degradation cost him as the race went progressed.
"I think you're always a little disappointed when you start first and don't finish first, but overall it was a good weekend for us," he told reporters.
"We had a good day today with a pole and a podium - but in the race we were a little too aggressive with the tires and lost the front and the rears, while others did a little better.
"There are always areas where you can improve, but the result we got today is fair.
"We didn't see Kimi on the track, he was too quick and Fernando (Alonso) jumped us at a vulnerable time - but we can be happy with third."
Meanwhile, Lewis Hamilton believes his opening race success with new team Mercedes is a sign of things to come.
Hamilton, who left McLaren at the end of last season, claimed a fifth place finish after teammate Nico Rosberg had suffered electronic problems on lap 26.
"I'm happy with our result today and it's much better than we expected for the first race of the season," Hamilton told reporters.
"The important thing is that we have a car that we can really work with and the team have done a fantastic job to get us to this position.
"Now we'll look forward to Malaysia and hopefully build on this positive start with an improved performance."
Hamilton's former team ended a miserable weekend with lead driver Jenson Button only managing a ninth place finish while new teammate Sergio Perez finished outside of the points in 11th.
"Having won the Australian Grand Prix three times so far in my career -- in 2009, 2010 and 2012 -- you'd have to say that today's ninth place isn't really much to write home about," Button told reporters.
"Having said that, I think we should be pretty satisfied with what we achieved in Melbourne today.
"It was a tricky race and our car isn't yet quick enough, so I think the team did a great job to achieve even as much as we did."
"Looking forward to Malaysia next weekend, I think we've got a tough few days ahead of us, but hopefully we can now do some number-crunching in an effort to understand our car a bit better and extract a bit more performance out of it there."