The former Championship club currently reside in the bottom three of the league table, taking just four points from nine games.
"I'm loving the challenge," said Adkins. "You only know once you're in a situation how you are going to react and face it.
"After the West Ham defeat there was a half-hour period which I didn't like but I'm loving the challenge that we are faced with. It is what you want to be in football for."
The Saints face West Bromwich Albion on Monday night.