Szczesny, returning after a two-game absence due to a rib injury, looked uncertain throughout and was directly at fault for Southampton's only goal when he failed to collect a routine high ball into the box, spilling it straight to Danny Fox who duly blasted in the first goal Arsenal have conceded so far this season.
However, the young goalkeeper retains the faith of his manager, with Wenger insisting Szczesny will continue in goal for the Gunners.
He told the club's official website: "Wojciech is No.1 unless I change my mind. That is clear. That’s why he came back in goal.
"You cannot change a goalkeeper every time he makes a simple mistake, because then you have three bad keepers. The confidence is needed."
Wenger went on to acknowledge the role played by Vito Mannone's form in Szczesny's absence as a cause for the latter's poor performance on Saturday.
"It’s a special position where confidence is needed," the 62 year old Frenchman said. "Maybe he put himself a little bit under pressure because he knows Mannone played well at Stoke and at Liverpool. I think he played better in the second half."