The result left Saints rooted to the bottom of the Premier League table and increased speculation Adkins' position is in jeopardy.
The manager is determined to fight on to try and turn things around but concedes his future is out of his hands.
"We need a win that's without question," Adkins told Sky Sports. "We've done it since I've been at the football club but it's about winning.
"I'm standing here a far better manager than when I joined Southampton and better than I was six years ago.
"I've got a hunger and a desire. I love being at Southampton. The supporters have been fantastic since I joined the club. I'm positive and it is my responsibility to lead from the front and I have every desire to go and do that.
"I can't control that (his future). It's a decision from the people at the top have to make."
Adkins felt Southampton were unlucky with Peter Odemwingie's first goal with the striker handling the ball in the build-up to the goal, but he admitted they need to improve their defending if they are to have any chance of staying up.
"We have gone and lost the game," added Adkins. "The first goal Mike Dean (the fourth official) is screaming down the mic that it's handball (against Peter Odemwingie) four or five times but he didn't pick it up.
"The second half we had a little better of the football than we did in the first half, but the goal we conceded was a poor one.
"We knew they were good on the counter. We gave the ball away too quickly."
Adkins continued: "Our desire to defend our goal has to better but unfortunately this season we have conceded far too many goals.
"Collectively we have to be forward thinking. We work hard on the training ground and we want that stability in the back four and our goalkeeper. We can score goals."