The German won the opening race of the season in Melbourne last year and backed it up with victory at the next in Bahrain. But Hamilton roared back to sweep 11 of the remaining 19 Grand Prix and the 31-year-old is desperate to turn the tables.
"There is a lot of passion inside this team willing to get out and to express ourselves through winning I think is the best we can do," he said.
"So that's the target. So far the atmosphere is good, the spirit is right within the team and we will try to carry that into the season."
Vettel is a winner and having to settle for second in the drivers and constructors championship last year was tough to take.
He said it was normal for Ferrari fans to consider finishing runner-up a "disaster".
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"You know the winner takes it all. Lewis has been in that position the last couple of years and we will try to turn it around," he said.
"In the end we are racing for Ferrari and we will try to get Ferrari back to where we've been trying to get it back to for the past few years." Ferrari haven't won the constructors' title since 2008 and their last drivers' crown came in 2007 through Kimi Raikkonen.
The Italian team have a new look heading into the season, with tech chief Mattia Binotto replacing Maurizio Arrivabene as team principal and young gun Charles Leclerc in for the experienced Raikkonen.
Asked if Ferrari were in a better situation now than 12 months ago, the 31-year-old replied: "Yeah quite frankly because last year's winter testing didn't go well for us.
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"We had some issues with the car to fix. We got a bit lucky during the race weekend (in Melbourne) with the safety car to grab the win.
"In this regard we are more prepared. Our car seems to work fine, there are no problems at this stage."
But he added: "It's a tough weekend ahead of us."
Despite his huge experience, Vettel admitted to being "a bit nervous" ahead of the 2019 campaign.
"You don't know exactly where you are, you don't know what's going to happen," he said.
"At this point we are all hunters and we are all the hunted. We have zero points."
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