John Button passed away on Sunday, at the age of 70, after suffering a suspected heart attack.
Button snr was an inspirational figure on his son's life and career, missing only one of the 34-year-old's 249 grands prix over the past 14 years.
The early weeks back in the paddock when the season resumes later this month, initially with the first test in Jerez and the opening grand prix in Australia in mid-March, are certain to be tough on the younger Button.
Three-times world champion Stewart, however, feels racing drivers over the years have proven themselves to be a tough breed and know how to adapt and survive.
"A racing driver is a peculiar animal," said Stewart.
"Look at all the deaths we had (during Stewart's time in the sport in the 1960s and early 1970s), yet for whatever reason we all raced.
"We had our wives with us, and with everything that went on on the circuit, many of them had to go to the track medical centre - which at that time was just a dirty concrete floor - to find their husband dead, or severely injured and going to die.
"Think about that, and then going to a funeral and meeting their mom and dad, brothers and sisters, and not just at the grave, but at the house afterwards. They were ridiculous circumstances.
"So when you think of John, naturally his son will miss him terribly, but a racing driver's mentality is a peculiar one.
"And the human is an amazing being to overcome those things, including grieving, with racing drivers tougher than most people."
Stewart, meanwhile, feels the time is right for the sport to usher in a new champion this year.
Sebastian Vettel and Red Bull have dominated the past four seasons, claiming both drivers' and constructors' championships, and with the German notably winning the last nine grands prix of last year.
"We've had domination before and the sport still survived, which was before the television era when there were bigger crowds," said the 74-year-old Scot.
"But it would be better, liven things up (if there was a different champion). It would be refreshing."
Stewart added with a smile: "And four times is a bit greedy.
"But nobody is up there forever, whether it's Sebastian or Adrian Newey (Red Bull's chief technical officer), whether it was Michael Schumacher or Ross Brawn.
"The world moves on and I'm sure that will be the case, although I don't know if it will be this year because Red Bull have been so impressive."