And the pair faced a tough test on Sunday afternoon as the Reds were welcomed by a resilient Saints side at St Mary's.
Southampton dominated proceedings against Rodgers' charges but, remarkably, Liverpool left the South Coast with all three points after goals from Philippe Coutinho (a wonderstrike) and Raheem Sterling secured a 2-0 win.
According to the Reds boss, meanwhile, his ex-Southampton duo performed admirably against their former club.
"When Dejan has been asked, he has come off the bench and had to do a job for us in the last few games and played very well," the Liverpool boss told reporters.
"Today was always going to be difficult but I thought he dealt with it very well. Adam Lallana was outstanding."
Southampton fans didn't make things particularly easy for their ex-playmaker, with the 26-year-old being booed by sections of the Saints crowd.
It didn't deter Liverpool, however, whose incredible form in 2015 has taken them to within just two points of the top four.
Things won't get any easier for Rodgers' men, though, with a trip to Turkey to face Besiktas upcoming this Thursday, before an Anfield clash with Manchester City next weekend. Southampton, meanwhile, travel to West Brom next.