Reading secured promotion to the Premier League on Tuesday night after beating Nottingham Forest 1-0 at the Madejski Stadium, but Adkins believes that his Saints side can still finish above the Royals.
"It was a thoroughly professional display and an excellent response to the defeat against Reading on Friday," said Adkins.
"We are not concerning ourselves with results elsewhere or the amount of points we may need to secure promotion.
"We have two matches left and we want to put six more points on the board. Our aim has always been to be champions and that hasn't changed."
Southampton travel to Middlesbrough and host Coventry City in their last two games of the current campaign.