Daniel Agger’s solitary goal was just enough to secure all the spoils for the Merseyside outfit in a game that saw the hosts pull the strings for the majority of the 90 minutes.
However, the last 10 minutes saw the home side succumb to clumsy passing a lack of concentration in possession that could have seen them lose vital points at Anfield.
Southampton had few chances on goal, but a late burst of energy saw them attempt to take advantage of their opponents' lack of concentration at the back.
Rodgers said of his team’s performance: "I thought we were outstanding in the first-half, the tempo and we shift the ball and everyone was passing and moving and the creativity was there.
"Throughout the game, it’s just that little bit of luck with the final ball, and no matter how much you dominate the game, if it’s still only 1-0 going into the final 10 minutes, it’s always going to offer you that wee bit of challenge and you’ve got to defend. Absolutely no question we should have been out of sight [at half-time]."
Striker Luis Suarez was booked in the latter stages of the game for a deliberate handball and when asked if he saw that as cheating, Rodgers replied: “I don’t think it was cheating. Once I see it, I’ll make a better comment, but if you’re saying was he cheating, I wouldn’t have said he was, no.”
The game with Southampton saw Liverpool midfielder Lucas return to the fray and Rodgers was more than pleased to the see the Brazilian back in the starting line-up.
He said: "I thought he was excellent; in my mind, he’s come so far in training and I felt I needed to get him into one of the games and he’s another piece to what we want to do here and you can see the difference he makes when he is in the team."
Nigel Adkins on the other hand was understandably downbeat about the match result and believed it was Liverpool’s confident movement and passing of the ball was the catalyst for their opponent’s success on Saturday afternoon.
He said: "We’ve come away from home and adapted, because we’re an attack-minded side and today we didn’t have nearly enough possession of the football as we usually do and that’s credit to Liverpool in all respect.
"We’re obviously disappointed in respect to the fact that we haven’t got anything from the game. We’ve come away from home on a good run of form of late and I think it’s fair to say that Liverpool’s movement was very good today and we couldn’t get a grip on the football."If we could have got to half-time 0-0 [and] still in the game, that would have been very pleasing; a free header in the area has given them a 1-0 lead."