The Reds lost 3-1 at the St Mary's.
On how much his side missed Carragher in the centre of defence, Rodgers said: "There's no question.
"For us, it's an area we feel we need to be better in. There's no doubt about that and that was one of the reasons for bringing him back - for his leadership qualities.
"But it wasn't the sole reason. We haven't been giving soft goals away like that for a long time now. That has given us greater confidence within the team."