Despite the loss, which is their second of the season, the Saints remain top of the Championship table.
"It wasn't our night," said Adkins. "We've got to make sure we're more ruthless to win games when those opportunities come.
"They worked very hard to deny us because we had a lot of possession of the football.
"When we reflect on it I suppose we will see we have nine games gone now and we are still top of the league, though I'm not looking at the league table, I'm just trying to throw a positive in there."
Southampton continue their league campaign on Saturday when they host Watford.