Earlier this month, Team USA fought back from 8-1 down against Team New Zealand to win sailing's most prestigious event 9-8.
Alonso is 60 points down on Vettel with six races to go and has not won a grand prix since May.
The Spaniard met with Ferrari president Luca di Montezemolo this week and both agreed that the team must keep pushing in the knowledge that anything is possible.
Alonso conceded, however, that he will need plenty of luck to beat Vettel.
"The president and me think anything can happen," said Alonso. "Like the America's Cup, we saw the American team was 1-8 down and they won 9-8.
"We know it would be difficult, but if you have two lucky races, things can change very quickly. But we need a lot of luck; we know that.
"We need to be realistic because we don't have the pace to beat them in normal conditions, so we need luck in all six races.
"If we have luck, everybody can be sure that we will be there to take [advantage]. We will not give up until it's mathematically impossible."
The Ferrari driver is also under no illusions for this weekend's race in Korea, which Vettel has won twice in three years.
"It will be a difficult weekend, but our hope is still to maximise the points," he added.
"If we can reduce the gap in the championship that will be welcome because now we have a very small chance to win the championship."