The Golden Globe-winning actor - whose performance in biopic Lincoln has also earned him a 'Best Actor' nomination at this year's Oscars - admitted that his eldest son previously believed he worked in the construction industry.
Speaking to The Mirror, he said: "They didn't even know what I was doing until a couple of years ago.
"In fact, my 14-year-old boy was asked what I did and he said, 'I think he's in construction'. That's how much they know!"
The 55-year-old went on to describe his parenting style as "old-fashioned" and confessed that he has tried to instil in his children the same values that his mother and father passed on to him.
"My parents believed in certain things, which I do too," he said. "I want my children to also. But there's no guarantee they will."
When asked about his role in the Steven Spielberg-helmed Lincoln, Day-Lewis - who has already won two Academy Awards for My Left Foot (1989) and There Will Be Blood (2007) and would make history with a third win - said that the most challenging aspect of filming was the make-up required.
"I was in complete denial," he explained. "It hadn't occurred to me I was going to need any make-up, so it came as a bit of a shock.
"I've tried to avoid using make-up over the years."
Watch a trailer for Lincoln below: