It took just 13 minutes for the visitors to take the lead at the Emirates Stadium and the Gunners had no reply after Ryan Bertrand's goal late in the first half
Arsenal failed to progress beyond the EFL Cup quarter-finals for the sixth season in a row as Southampton beat them to a semi-final spot with a 2-0 win at Emirates Stadium.
First-half goals from Jordy Clasie and Ryan Bertrand did the damage for Southampton, who had lost 2-1 on this ground earlier this season in the Premier League.
The League Cup remains the only domestic honour Arsene Wenger has never won with Arsenal, but there was little sign of an appetite to change that on Wednesday.