Hammond and James May followed Jeremy Clarkson to Amazon Prime Video after Clarkson parted company with the BBC for punching a producer.
In an interview with the Daily Telegraph, Hammond, 46, spoke of the pressure of their latest motoring show, The Grand Tour, and dismissed “mad speculation” over each episode’s budget, which has been reported to be up to £4m (€4.6m).
“We’re not going to disappoint, because we can’t,” said Hammond.
“We’ve got to make this good or they will come and torch us — and rightly so.”
The show’s format sees the trio dispense with the usual television studio and tour the globe, hosting each episode in a large marquee in different locations.
The show is set to take in cities including Los Angeles, Stuttgart, and Johannesburg as part of its tour.
Hammond also refused to be drawn on his thoughts on the latest series of Top Gear, which saw the outgoing presenters replaced with Chris Evans and Matt Le Blanc.
Evans announced his departure from the series in July, having hosted just six episodes.
Last weekend, Clarkson appeared on The Jonathan Ross Show on ITV, where he described The Grand Tour as an “adolescent” Top Gear.
However, he insisted that it’s a different programme because of the BBC’s hold on his original show’s intellectual property.
“So lawyers come and say ‘You can’t do that, you can’t have the audience standing up, you can’t do Star In A Car, you can’t have The Stig, James May can’t be slow and pedantic, I can’t be bombastic, Hammond can’t be short and from Birmingham’ so we had to jumble everything up and so we had to start again,” he said.
“The BBC owns the show,” Hammond told the Telegraph.
“But ultimately, I own the copyright on me, I’m my own intellectual property, as are James and Jeremy.
“No lawyer can argue that I can’t be short any more because I am.”
The Grand Tour makes its debut on Amazon Prime Video on Friday.