Three goals against the run of play at St Mary's have seen the Royals leapfrog the Saints at the top of the Championship table.
"Well done to Reading because they've come to our place and they've got three points, but from our point of view, we've gifted them three goals," Adkins told Sky Sports News.
"Our principals will never change but it's about, as I say, winning the games of football.
"But what we've got now is three games to go. We remain positive. We've got three games where we're going to be positive in everything we do and strive to win those games."
The loss has left the Saints six points above third-placed West Ham United, who have a game in hand.