Jay Rodriguez and Adam Lallana scored either side of the interval for Mauricio Pochettino’s Saints, who inflicted a seventh successive defeat on the Royals.
Though rooted to the foot of the table and now eight points adrift of safety, Adkins remains focused on survival and is adamant that the team will continue to work hard in their remaining fixtures.
“We are where are. We have to be realistic and face the reality of that,” the 48-year-old boss told reporters after the match.
“But everyone at Reading is going to work very, very hard and we look forward to the next game.
“What we’ve got to do is analyse the game with the guys on Monday, debrief, take the positives from the game, learn the lessons and work very hard on the training ground ahead of the next games.
“That is important and the process we have to go through to give ourselves the opportunity to win the next game.”
Southampton opened the scoring in somewhat controversial fashion, as Rodriguez dived into a challenge to prod the ball past Adam Federici, and Adkins felt some of the major decisions had not gone his side's way.
He continued: “I think if you look at the players, especially in the first half, they have put in a lot of effort out there.
“They had a go and maybe on another Alfie’s [Adam Le Fondre] shot goes in or the referee maybe gives a free-kick for the challenge on the goalkeeper or the linesman puts the flag up for offside when they score.
“The referee might give a penalty decision from the challenge from Jos Hooveld or not as it didn’t happen in the game.
“Is Le Fondre’s header over the line when Artur Boruc has saved it? I’ve just seen it and it looks like it is 99.9% over the line. It’s not given.”