The reigning world champion finished 22 seconds adrift of race winner Kimi Raikkonen, and he was unable to live with 2012 title rival Fernando Alonso either after starting the race on pole.
But Vettel believes third place was a fair result for the season opener.
"We can be happy with today," he said. "Clearly we wanted more, when you start from pole you want to win.
"I'm not worried, we have to admit sometimes that other people are faster. We were the third fastest car in the race today."
The Red Bull driver added that he was surprised to learn that Raikkonen was ahead of him, but he was pleased to make a solid start to his season after a race made tricky by tyre management.
"After a good start and first two-three laps the tyres were falling apart," he added. "We couldn't go as long as other people.
"I knew Fernando passed us at the stop, and I didn't know where the other car [Raikkonen] had come from. I never saw him so it was a little bit of a surprise.
"We have to be happy today. We have good points. It was good fun, tricky with tyres, but I'm happy to be on the podium."
Vettel spent several laps stuck behind Adrian Sutil's Force India as his countryman went for an alternate strategy, but he doesn't believe that made a crucial difference to his result.
"It did not help at that stage, but it's pretty simple - if we had the pace we should have passed him," said Vettel.
"I don't think considering all the laps in the race it made a massive difference. In the end you have enough laps to even things out."