The 33-year-old endured a torrid campaign with the Italian heavyweights, earning a place on the podium just once in 17 attempts as the Prancing Horse limped to a sixth-placed finish overall.
The car’s lack of ability to compete, along with a number of individual mistakes, curbed Vettel’s hopes of returning to the front of the grid.
He was visibly frustrated on a regular basis throughout the season amid the deterioration of his working relationship with Ferrari.
However, the new campaign has renewed his hopes of fighting for race wins, with Aston Martin expected to trouble Red Bull and Mercedes once again after an impressive fourth-placed finish last time out.
JUST IN: George Russell clarifies Toto Wolff stance on promotion to Mercedes
The German declared that during his time with Ferrari, Mercedes were the only team strong enough to fight for titles, suggesting that Hamilton’s success in F1 has been aided significantly by the machinery underneath him.
“I think I can [win another title],” said Vettel. “Obviously, I am not too old. There are now older drivers joining the grid rather than younger drivers.
“I don’t think it’s an age thing. I just think it’s more of a question of, do you have the team around you?
“I think we were close with Ferrari but never really close enough to have a say in the last two or three races so I don’t think it’s an age thing. I think it’s [another world title] in me.”
Vettel and Hamilton became embroiled in an intense championship battle during the 2017 campaign, when their competitive rivalry came to a head.
The pair clashed on the track at the Azerbaijan Grand Prix when Vettel appeared to deliberately swerve into Hamilton under safety car conditions.
Vettel hailed the Stevenage-born racer at the end of last season, claiming that he is the best driver of his generation after sealing the Drivers’ Championship crown once again.
“I told him it’s very special for us because we can witness history being made today,” Vettel told reporters after November’s Turkish Grand Prix.
“I think he is the greatest of our era for sure.”