Hull have won three of their opening six Championship games and are now preparing to host Leeds at the MKM Stadium on Wednesday night.
Leeds have won just two league games thus far but they are being backed as one of the favourites to get promoted and did beat Millwall at the Den on Sunday.
Rosenior stressed the importance of grabbing the bragging right by beating Leeds this week as it is important for Hull as a club and their fans.
The Hull boss insisted that games against Leeds are very different to any other and is hopeful that his players will rise to the occasion in the hot atmosphere the fans will create at the stadium on Wednesday night.
Rosenior told BBC Humberside Sport: “Leeds are a big club and we are a big club.
“Geographically, there are bragging rights and I played in a few games against Leeds as a player here and they are different.
“I am really looking forward to seeing how my players, hopefully, rise to the atmosphere.
“It’s going to be a red-hot atmosphere; I know the fans are going to be fantastic as they were against Coventry and I am really looking forward to it.”
Leeds have shown good form on the road early in the season and have won two of their three away league games.