The newly-promoted side were handed a less-than-kind opening run of fixtures, and as a result have managed to record just four points from nine games and sit second bottom of the league.
However, the 47-year-old is remaining defiant and has indicated that he will instruct his players to be positive and stick to their style of play.
He told reporters: "I'm loving the challenge, you only know once you're in a situation how you are going to react and face it.
|16/1||Southampton are 16/1 to beat West Brom 1-0 with Bet365|
"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."
Despite leading Saints to back-to-back promotions in the previous two seasons, Adkins' job has been reportedly in the balance in recent weeks due to Saints' poor form.
But the former Scunthorpe manager believes he has been touted as an under pressure manager since before the season began, and assured fans that nothing has changed since.
He added: "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."