The Frenchman equalled the best result in his grand prix career last time out at Austin, withstanding a late Mark Webber charge to clinch second.
And while Vettel's control of the race was never under threat, Grosjean says he has not abandoned hopes of beating the German in this weekend's Brazilian finale.
"Thinking that we can win the race - that is why I am here," Grosjean said.
"It is what we are aiming for.
"After Friday and qualifying we have to assess where we can be, but it is always an eventful weekend so we can hope.
"The best chance for us is to keep pushing hard and putting pressure on our rivals, and try to get them that way."
Grosjean said that it was an incredible achievement to simply split the Red Bulls in the US, but said the clear advantage Vettel and Webber currently enjoy was no cause for despondency.
"Even finishing second at Austin was extraordinary, looking at how the Red Bull performed," he added.
"I am proud of what I am doing; I don't think I can do more."
Grosjean has taken four podiums from the last five races, a record only bettered by Vettel.
He is assured of seventh in this year's F1 drivers' championship regardless of where he finishes at Interlagos.
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