Di Matteo was appointed to succeed Jens Keller earlier this month and has led the club to two wins and a defeat in his three matches in charge in all competitions.
Speaking shortly after his appointment, Di Matteo declared that he would have the final say over team affairs and Heldt has supported the former Chelsea chief's bid to stamp his authority.
"Absolutely, he has the responsibility as a coach, so it is important that this is seen," Heldt told Die Welt. "This does not mean that he does not allow for other opinions, but in the end he decides.
"Not only the team concept is important, but also a clear hierarchy. This was one of many reasons why we decided to appoint him."
And Heldt believes Schalke can be confident of a bright future on the domestic front.
"In the last decade, FC Bayern have become the masters," he added. "[But] Schalke have been three times runner-up in that time.
"The past has shown that it [a title push] is possible. Schalke is a club that has a lot of power and lots of options, so it will be possible in the future."