The Steelers were beaten 55-31 by the Patriots in their last game, but Marrone said that score just means that Pittsburgh will be extra motivated against his side.
"Well I think the first thing that comes to my mind and how much respect I have for Mike Tomlin is that they are going to come back and they are going to get after it," Marrone told the club's official website.
"They have a lot of pride in that organisation, a lot of pride in that program and a lot of pride in that defense. A lot of those players I have even faced when I was coaching in the league even though I took four years off.
"There is a lot of pride in for that defense in Pittsburgh. They are going to come back and they are going to be ready to go. We will get their best game."
The Bills are 3-6 for the season, while the Steelers are 2-6 having had their bye week.