Daniel N’Lundulu netted an early brace for the hosts, before Jake Vokins and Will Ferry added to their lead in the second period.
Rogers pulled one back before N’Lundulu completed his hat-trick with just under 15 minutes remaining. Rogers added to his tally with a late consolation as the clock ticked towards stoppage time.
Enzo Maresca’s EDS side were immediately put on the back foot by the Saints at the sunny Staplewood Training Centre, with the hosts signalling their intentions early on by winning a quick corner.
We managed to clear but in the sixth minute Southampton found the net, with N’Lundulu racing clear after being put through by Nathan Tella and slotting beyond Cieran Slicker.
Before the City youngsters had time to regroup, the Saints were celebrating a second, N’Lundulu pouncing again from close range to double his side’s lead in the tenth minute.
It was the worst possible start for the in-form City youngsters but we managed to settle down as the clock reached the half-hour mark and began to stroke the ball around with more confidence, pushing the Saints’ backline deeper as the half wore on.
However, the hosts began the second period just as they did the first, and netted a third in the 54th minute, with Vokins powering a header beyond Slicker after an accurate delivery from Yan Valery.
Just after the hour mark, Slicker was picking the ball out of his net for the fourth time of the afternoon, as Ferry coolly slotted in from Tella’s clever pass.
Two minutes later, Rogers provided us with a glimmer of hope, finding the back of the net after being found by James McAtee.
As Maresca’s side pushed forward to try to half the deficit with just under 15 minutes remaining, the Saints picked us off as N’Lundulu latched onto Vokins’ pass and netted again – completing his hat-trick.
Rogers got his name on the scoresheet again in the 89th minute, but quite simply, it was too little too late.
What it means
City remain seventh in the Premier League 2 table, two points ahead of Manchester United and one point below Brighton and Hove Albion, who have played one more league game.
How we lined up
Cieran Slicker started in goal, shielded by a back four of Alpha Diounkou, Taylor Harwood-Bellis, Luke Mbete, and Nathanael Ogbeta.
Claudio Gomes operated in defensive midfield, supported by skipper CJ Egan-Riley and James McAtee, with Morgan Rogers and Jayden Braaf providing the width for frontman Liam Delap.
Due to the international break, our EDS side is out of action for ten days, playing next on Tuesday 17 November in the Leasing.com trophy, facing League One side Lincoln City at the LNER Stadium. Kick-off is scheduled for 19:00 GMT.