The Manchester United and England star saw his side go two down before pulling back.
However, a killer blow by Adam Armstrong five minutes before the end sealed the Blues fate.
Rooney was given positive backing by travelling fans, and believes his opponents can show how to turn fortunes around.
He said 'It's going to take time, Southampton are a perfect example – Russell Martin has a clear way of playing, it's similar to how I want my teams to play.
Wayne Rooney has overseen three successive defeats since taking charge of Birmingham
Adam Armstrong scored his eighth goal of the season to seal a 3-1 victory for Southampton
Taylor Harwood-Bellis opened the scoring for the hosts with an eighth minute header
'You need time to get the confidence into the players to do that.
'I'm patient, I'm a calm person, no doubt that will come.
'At the moment we need to pick up points, that's for sure, but I'm in no doubt they will come.
'I'm disappointed to lose the game, the three goals were bad goals to concede.'
Southampton took a tenth minute lead when Taylor Harwood-Bellis headed home his first Saints goal.
It looked a rout on the south coast on 23 minutes, when Carlos Alcaraz poked home a Kamaldeen Suleman cross from close range.
Birmingham hit back in the second half when Jay Stansfield – on the field for just 52 seconds – broke through to curl into the top corner.
Although the goal fired up Birmingham, the last word fell to Southampton and Armstrong, who neatly struck home with five minutes remaining.
Victory leaves the Saints six games unbeaten, and manager Martin was left pleased.
He said 'It's been a really nice run, especially on the back of the run that came before that, which makes me even more proud of the players and the staff, how they've come through that period.
'The growth in the team in the last few weeks has been incredible.'
Carlos Alcaraz scored his first of the season to double Southampton's lead in the 22nd minute
Jay Stansfield scored less than a minute after coming on as a substitute for Birmingham