The full-back has been a pivotal figure in The Tigers defence, helping to keep three clean sheets in four games at the KC Stadium in the Premier League.
A string of impressive performances has seen Hull's unbeaten run stretch to five games in all competitions and Rosenior says that they have the quality to avoid the drop.
"I expect us to stay up. I expect us to win every game if we can," he told the Hull Daily Mail.
"The Premier League has learnt that we're going to be a hard team to beat. We don't lie down for anyone and we give our all every game.
"You won't see too many teams beating us by four or five this season, that's for sure."
Rosenior believes that there is more to the team than impressive defensive displays, highlighting the work rate of the City frontline and the strong mentality throughout all areas in the team.
"You look at Danny Graham and Sone Aluko starting up front, and they work their socks off for us up there. We had Stephen Quinn and Ahmed Elmohamady tracking back all the time.
"We already had a good squad. We must have done something right because we got promoted, but that mentality has continued where we pick up points whether we're playing well or not.
"Curtis Davies has taken on the captaincy, but if you look around the team you could have five or six different captains.
"We're working hard for each other and that needs to continue if we're going to pick up points."
Rosenior will be aiming to continue their unbeaten run after the international break, with The Tigers facing tough back-to-back away games at Tottenham and Everton.