Saints returned to second spot behind Brighton after ending the champions` unbeaten home record with a 2-1 victory at the Withdean.
Goals in the last five minutes from substitute David Connolly and defender Jose Fonte turned the game on its head after Ashley Barnes had fired Albion ahead on the stroke of half-time.
Adkins believes his players must not get distracted by getting too ahead of themselves, and said: "For us it's got to be in the here and now. We're looking to get this magnificent club into the next division and for that we must take care of business.
"We had five games called off, we've had to play catch up and towards the end of the season there are lots of twists and turns."
He added: "Brighton put their best team out but our game plan was right and we played the match on our terms. We conceded a shocking goal but had so many opportunities in the second half and deserved the victory."
Source: PA
Source: PA