The south-coast club sit 12th in the table with 34 points from 30 games, six points off the drop zone.
"We did something similar last year and then went on an incredible run after that. We won five games in a row," Rosenior told the club's website (www.brightonandhovealbion.com).
"It would be fantastic for us to be safe going into the last five or six games, and just be able to enjoy the games and focus on performing well, without the added pressure of relegation."
Brighton have enjoyed a good run at home this season with 24 points from 15 games, losing only to champions Chelsea, Liverpool and runaway leaders Manchester City.
"In terms of our confidence, we've improved as the season's gone on. That's a natural thing that happens, we had a lot of players without Premier League experience," Rosenior said.
"I couldn't wait for those players to realise they were good enough to play at this level, and I think they're now showing that in their performances."
Brighton host eighth-placed Leicester City on Saturday.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond)
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