The Saints became the first club to score three first-half goals away at Stoke in the Premier League as they dominated the opening 45 minutes.
Despite Cameron Jerome's wonder goal late on denying his side all three points, Adkins believes that his players deserve credit for matching their opponents.
"We did fantastically well," Adkins said.
"We have come away from home and quietened a vocal crowd, and our supporters could be heard all round the stadium during the first half.
"We scored three very good goals, and not many teams will do that as Stoke have only conceded four at home this season.
"I thought we were dominant during the first half and we had an opportunity to go four up. They have scored a wonder goal but I am pleased.
"It was top drawer. We have not come away with three points but we have come away with something."
The result sees Southampton drop into the relegation zone after Wigan Athletic won away at Aston Villa. The Saints do have a game in hand on their rivals.