Two goals from Peter Odemwingie either side of the break condemned the Saints to their eighth defeat in 10 games, adding more pressure on the 47-year-old.
However, Adkins said that he is still hungry for success on the South coast and remains "positive" about his future with the club.
"I'm standing here a far better manager than when I joined Southampton and better than I was six years ago," Adkins told Sky Sports News.
"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."
Adkins took control of Southampton when they were in League Two in 2010.