Steven Fletcher's strike three minutes before half-time proved the difference on the south coast as the Black Cats held out for a 1-0 win in difficult conditions at St Mary's.
"It just didn't happen for us," Adkins said. "For me, it was uncharacteristically flat for whatever reason.
"Obviously I will digest that and with the goal we conceded just before half-time, there are two or three people that could have done better in stopping the goal.
"That has obviously given Sunderland something to hang onto in the second half and, to give them credit, they defended well.
"We tried to change things around early to give ourselves an opportunity to increase the tempo, find a way forward, stretch the game to create openings, but unfortunately we haven't scored any goals."
Southampton looking devoid of ideas going forward without influential captain Adam Lallana, who picked up a knee injury against Reading last time out.
"It can't be about one player," Adkins said. "Every team is going to have players that are missing.
"You have got to have a strong enough group of players that can go and contribute. Who is to say if Adam had played it would have been any different?
"We played Gaston Ramirez on the left-hand side, where he plays for Uruguay and does that very well. We can't just turn around and say that losing one player caused the result."
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