The 46-year old, who led the club out of League One at the end of last season, is now looking to achieve back-to-back promotions as his new and improved side target the Premiership.
"There will be an improvement but you can't underestimate the spirit and the team ethic," Adkins told the Echo. "That can take you so far and then you've got to get the quality and we have certainly got quality players.
"We are on the right footing, we are moving forward, I think we are endeavouring to play quick, passing football.
"It's a process of getting stronger and fitter and it's in our programme that we make sure we are in the race come January. And from there on in, can you give yourselves a chance to win the race?"
Southampton begin the new season at home against Leeds United on Saturday.