The Seagulls suffered a blip in their survival campaign as they let a 1-0 lead slip.
Solly March broke the deadlock early in the second half before Bournemouth's Jordan Ibe came on to assist goals for Andrew Surman and Jermain Defoe.
Rosenior: We were in control
After a very pedestrian and slow first half, the game sprung into life in the second with March's headed opener. Brighton had kept Bournemouth at bay for large parts of the game but the Cherries manager, Eddie Howe opted to introduce record signing Ibe.
The £16million man came on and back heeled to Surman who finished and then sent Defoe clear to secure the second-half comeback.
Rosenior has spoke about the lessons learned from the Cherries loss and believed his side were in "control" when they were 1-0 up.
Speaking on the Albion's performance Rosenior said: " I think this is a lesson for us. You can't switch off, you can't give away cheap goals.
"Maybe we felt too comfortable and took our foot off the gas, you can't do that in the Premier League."
Away form the key
The seaside club won 11 of their 23 Championship away games last season and Rosenior hopes that they can emulate that away form this time round.
He said: "We are very solid away from home, we know we will get chances on the break."
The defeat leaves Brighton level on points with the bottom three with only goal difference setting them apart.
The former Hull City defender rues the defeat and he cannot help but feel that they have been hard done by.
He claimed: "Two bits of quality from them and they have won the game."
The Seagulls can seek avenge on Tuesday when they travel back to The Vitality Stadium for their Carabao Cup fixture against Bournemouth.