The Saints securing automatic promotion last season, finishing just a point behind champions Reading, but face a daunting opening fixture away to champions Manchester City.
However, their boss is excited about the challenge and feels that his side can impress in the Premier League as both Norwich City and Swansea City did last season.
"Everybody should be looking forward to it, enjoying it," Adkins told The Independent.
"People questioned [striker] Rickie Lambert before last season, his first in the Championship, and look how well he did. You have to have belief, go and grasp the opportunity that we have worked very hard to get.
|6/1||Southampton are 6/1 with William Hill to finish in the top half of the 2012-13 Premier League|
"Not everyone was expecting us to do as well as we did in the Championship, but we were in the top two the whole season – on merit. Yes, we are going to the next level, but there is a stability here that should give us strength. You can't underestimate team spirit."
Adkins also spoke of his feeling that the club have a bright future, which will be welcome news to fans following Southampton's financial troubles in recent history.
"As a manager you sometimes think of winning the next game and needing money for a player, and you forget about the heart and soul of the club," he added.
"If we get the structure right then there'll be a production line for many years to come of players playing the Southampton way, which will be financially right for this club. Whether I am still the manager at that time is another question, but you've got to think above that.
"We have to go into the Premier League with the belief that we can be strong in it. Aiming for 17th place is wrong. If you just fall short of it, there is a consequence. Aim higher, and if you fall short of that you've done all right."