Rosenior has praised the spirit within the squad as Bruce’s side look to build on back-to-back wins in the league.
Hull are just one point clear of the relegation zone and face three of the current top six in their remaining four games.
The 30-year-old believes the team have found their identity and have the ability to escape the drop.
“The most important thing now is that complacency doesn’t come in,” said Rosenior.
“I’m sure with the manager and the coaching staff and the players that we’ve got here there won’t be any complacency until they get the job done.
“It’s not who is under pressure but who deals with the pressure better. It’s a horrible thing to go through, to be honest it’s what makes the league so great.
“In American sport you don’t have promotion or relegation, to see teams like Bournemouth promoted that’s what it’s all about, it’s great but I just want to make sure for the rest of my career I stay in this league and not the one below.
“To have the players that have been promoted here, there’s a soul in the team and [Arsenal] will be a difficult test for us.”
Watch Hull City v Arsenal live on Sky Sports 1 on Monday at 8pm