Russell Martin's visitors showed promise, but a soft underbelly cost them in the 24th minute when Taylor Harwood-Bellis failed to deal with a hopeful ball to Duran and the striker raced clear to score.
"I love Taylor and I don't want to criticise him, but what happened can't happen," said Martin.
"Smooth the game out and pass the ball to a team-mate or you defend and clear it and we did neither. The goals we concede are so poor."
Southampton also failed to manage a shot on target and are the lowest scorers in the Premier League with just 11 goals.
"It's madness," said Martin. "We had one where Flynn [Downes] is in the middle of the goal, Cam Archer is in the box.
"I don't know what more I can give to the players to make them believe and that extra spark.
"Other than stop the game and tell players how good they are and what they can go and do, it's just that bit of spark and belief in the final third."
Duran's goal was the highlight of a forgettable game. Villa did not need to be at their best and Southampton lacked the quality to recover from conceding another sloppy goal.
Villa were able to collect only their second clean sheet in the league this season and goalkeeper Emi Martinez was never tested.
The hosts allowed the game to drift in the second half, unable to build on their lead, but they were never in serious danger and Joe Lumley denied John McGinn the chance to make victory more comfortable in injury time.