The Saints never really got going in a game during which they had just two shots on target, and were felled by a first-half finish from Steven Fletcher.
Adkins conceded that his side had failed to demonstrate enough creativity to justify anything from the game after Sunderland had scored.
"It was uncharacteristically flat from us today," said Adkins.
"Whatever we tried to and endeavour didn't give us the opportunity to score goals today.
"The goal we conceded before half-time we should have done better with, and it gave them something to hang onto.
"They did that very well."
Southampton only sit outside the relegation zone on goal difference, although they do have a game in hand on their rivals.