Prince Charles hopes he will be appreciated "a little bit more" for his contributions to UK life, including the Prince's Trust, when he is dead.
The US trip will be the couple's first joint official overseas tour
He was speaking in an interview for television channel CBS, ahead of next week's official tour to the US.
It is a first overseas engagement with his new wife, the Duchess of Cornwall.
Before leaving on the eight-day trip, the prince will host the National Hedgelaying Championship at his Gloucestershire farm.
In the interview for 60 Minutes, to be aired in the US on Sunday night, he told the channel's Steve Kroft that his charity, the Prince's Trust, which gives job training to young people, would not have been possible without his efforts.
"I try (to make a difference)," he said.
"I only hope that, when I'm dead and gone, they might appreciate it a little bit more."
It was important "to be relevant", he said in the interview, filmed last month in the village of Poundbury, Dorset.
"It isn't easy, as you can imagine, because if you say anything people will say, 'it's all right for you to say that'.
"It's very easy to just dismiss anything I say. It's difficult."
Being relevant meant putting "my money where my mouth is as much as I can", Charles said.
Poundbury, a village he developed built of recycled and natural materials, was one example of this.
Charles said one of his duties as a royal was "worrying about this country and its inhabitants".
"And I find myself born into this particular position," he said.
"I am determined to make the most of it."
The royal couple's week-long visit to the US, which begins on Tuesday, will include visits to New York, Washington and San Francisco.
In New York, they will inaugurate a new memorial garden for the British victims of the 11 September attacks.
And in Washington they will lunch and dine with President George W Bush and attend a youth event at the United Nations.
The couple will not be staying at the White House, although details of where they will stay have not been released for security reasons.
Meanwhile, before the trip, Prince Charles will play his part in rewarding Britain's best hedgelayers.
About 130 hedgelayers from all over the UK will compete at Home Farm, in Tetbury, using a variety of local styles to construct the traditional barriers.
The prince will present the prizes at the championship, co-sponsored by the Rural Development Service (RDS), part of the Department for Environment, Food and Rural Affairs (Defra), on Saturday afternoon.