The skipper revealed the mood of the changing room back at Spurs Lodge as the lads begin the road to recovery after the 4-0 defeat at St Mary's.
"The lads are embarrassed about the scoreline," he said. "You can go out of the FA Cup through a little misjudgement or being unlucky but when you've been beaten 4-0 it's embarrassing and something we want to put right."
Teddy said the performance was down to not starting well and being hit hard by quick goals after the break.
"We started badly, didn't get into our stride at all and before we knew it we were a goal down and we couldn't recover," he reflected.
"They were at full steam and it just shows you that if you don't start the game at the right tempo then it is difficult to catch up.
"It wasn't a case of losing belief, but losing the second and third goals in the second half really knocked us back.
"Obviously we didn't play well but we were happy to go in at 1-0 down at half-time.
"You then think 'if we can get a goal early, the goal will change around' but they scored early and that knocked us back.
"Having said that we had chances before those goals, in fact before, during and after. If we take one, the game can change around but it didn't run for us on the day."
Teddy Sheringham says the players are 'embarrassed' by the FA Cup exit at Southampton and determined to put it right.