The Saints claimed a crucial 3-1 victory over promotion rivals Bournemouth on Saturday to leapfrog them into fourth place, 10 points behind leaders Brighton.
But, despite the significant gap, Adkins is confident his side can finish top of the pile.
"We want to be successful, we want to win this division, we want to get promoted, but we've just got to take it one game at a time," he told the Southern Daily Echo.
"There's 12 games to go for ourselves, and that's a long, long way - and they're exactly the same. From experience, I know every game from here on in starts to take on a special significance and a special meaning.
"From Brighton's point of view, it's so near yet so far."
Source: PA
Source: PA