Adkins takes his side to West Brom on Monday night still searching for an elusive league win.
The former Scunthorpe manager has come under increased media speculation regarding his future at St Mary's but revealed he is loving life at the wrong end of the table, with Southampton sitting 19th with only four points on the board.
"I'm loving the challenge, you only know once you're in a situation how you are going to react and face it," he said.
"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."
Adkins feels he has been a marked man even before the Premier League season got under way but does not feel under any more pressure now than when he was guiding the Saints to back-to-back promotions.
He said: "Before we even kicked a football I think I was the favourite to be sacked.
"So every week there is a question about that and it doesn't faze me one iota, I'm very, very ambitious and we are very ambitious here at Southampton - what will be in football will be.
"(The pressure) is exactly the same as when I joined. I put my comments out straightaway that I wanted to win the league and we got ourselves promoted, then we got ourselves promoted from the Championship.
"We are ambitious, we want to be winners and we are used to being winners - we are now faced with a different challenge but it is one that we embrace, we look forward to it. Nobody said it was going to be easy, this is what we are in football for, we are pushing ourselves to the limit.
"We can go one of two ways - we can either hide behind situations and crumble or we can face everything up, stick our chests out and we can be positive in what we do."
Norwich set an example last season of a side who can sustain a place in the top flight following two consecutive promotions but Adkins is keen to stress the club are still in a transitional period after dropping into the third tier.
"We have come a hell of a long way in a short space of time, I think everyone is well aware of that," he said.
"It is quite often the way that a newly-promoted side from a defensive point a view, a lot more questions are asked of you when you move up - especially if you have jumped up two divisions like we have gone and done.
"Everyone wants to the finished article straightaway, there is a great work in progress that is going on here at Southampton.
"There a lot of people from top to bottom throughout all of the different departments work very hard and are proud to be here at Southampton."
Adkins feels a number of injuries to key personnel over the opening months of the season have also played a part in destabilising his side.
"I never want to harp on about injuries but it is fair to say that the back four has been unsettled more or less in every game for one reason or another," he said. "I'd like to think we can now put a consistent back four together and that will only add to the stability in the team."
One player due to return from injury is club-record signing Gaston Ramirez.
The Uruguayan has been missing for five weeks with a thigh injury after his summer move from Bologna but Adkins is hoping he can unleash the 21-year-old at the Hawthorns on Monday night.