The Tigers reached the FA Cup final in May, but their league form tailed off to the extent that a run of seven defeats in their last eight games saw them finish in 16th place.
Steve Bruce’s side will also have Europa League football to contend with during the forthcoming campaign, but their 30-year-old defender wants to tap into the spirit that defied those who believed they would head straight back to the Championship following their promotion in 2013.
"This time last year we were talking about what a tough challenge the Premier League was going to be but we managed to overcome that," said the former Fulham and Reading player.
"The mentality that we have, starting from the manager and working down though the coaching staff, is to prove people wrong. That's in our make-up and hopefully we can do it again this year.
"The first target has to be to stay up. A second season in the Premier League can be difficult.
"What happens is teams find out about your strengths and weaknesses. There's nowhere to hide or surprises.
"It's going to be a harder season this year than it was last year. We've got to expect a tougher challenge and make sure we keep on improving."
The Yorkshire club will make their debut in European competition in the third qualifying round of the Europa League, and Rosenior is excited to be heading into uncharted territory.
"We could start the season anywhere around Europe but that's part of the fun," he added.
"When you're a young player you want to play at the highest level and Europe will be another new one for a lot of us.
"This is another thing for our CVs. We want to at least get to the group stages. We don't want to be knocked out in the qualifying rounds. To make sure that doesn't happen we have to be fit and ready for July 31."