The Capital duo have had to hand back 12,000 tickets for games against the Old Firm.
Hibs have had their allocation cut from 17,000 to 10,000 for their clash with Celtic on the Saturday, while Hearts have had to return 5,000 tickets, which means they will have 12,000 at most in attendance for the fixture with Rangers the following day.
The pair have been left unhappy at the timing of the cut and the fact some fans will have to be pay for the most expensive tickets.
Yet, Stewart sees the situation as "a sad indictment of the way things are at two of our biggest clubs at the moment" that they have struggled to sell their respective allocations.
Writing in his column for the Scottish Sun, he said: "And the worst thing about it for me is it’s actually not that surprising.
"You just get the sense that Hibs and Hearts fans are totally and utterly scunnered with their sides right now. There’s not even a sense of anger, more an acceptance things will get worse before they get better.
"And when you look at the league table and see them sitting tenth and 11th? Well, it’s hard to argue. These two, along with Aberdeen, are the clubs you expect to take the fight towards the Old Firm.
He added: "It just shows the apathy their own fans have towards them right now. And that should worry Ann Budge and Ron Gordon, because that’s not something that’s easy to fix."
Stewart has been a well-documented critic of Hearts boss Craig Levein for a number of months but he is willing to give Hibs boss Paul Heckingbottom more time.
He said: "Hearts fans, in particular, seem to have given up and accepted nothing is going to change anytime soon.
"Hibs are in a similar position — but I’m willing to cut Paul Heckingbottom slightly more slack.
"The Yorkshireman is still relatively new to the job compared to the time Levein has been at Tynecastle. And Hibs haven’t had the same infrastructure in place like their rivals have for the past five years.
"But there’s no doubt with each passing week the goodwill towards him is disappearing."