Victory not enough to reach Second Round.
Earlier defeats had already made it impossible to progress into Round Two, however a very young U's side ended on a high.
It was the final group stage game for the U's, but the win at Florence Park wasn't enough to keep them in the competition.
The U's have beaten Southend 2-1 in the Central League Cup.
Femi Akinwande got a winner for the U's though, manufacturing the chance himself with good individual skill in the Shrimpers' box.
Southend came back at the U's at the start of the second half and got a deserved equaliser.
After being gifted possesssion, his initial chipped effort hit the post but he was quickest to react and put in the rebound.
New signing Eli Phipps got the U's on the way with a first half opener, when he capitalised on a defensive mistake.