Although the Royals began brightly and created a number of openings, Jay Rodriguez got the first in the 34th minute and Adam Lallana made sure of the win 18 minutes from time.
The win lifts Southampton seven points clear of the drop zone, while Reading are seven points adrift of safety at the foot of the table.
"We needed a win," Adkins said. "We were up against a good team but we're at home and we've got to win the game of football. We've not done that, that's the reality of where we are. We've got to keep working hard."
Reading were left to rue a glaring miss by the usually reliable Adam Le Fondre when the game was still goalless, but Adkins was not pointing a finger of blame.
"He's a great goalscorer in my eyes, a great finisher," he said. "We've got him on the field for that reason so when the opportunity comes he can take it. It didn't happen here but it will in the future."
Reading now have six games to somehow overhaul a number of clubs if they are to play Premier League football next season.
"It's a situation we don't want to be in, but we're in it," Adkins said. "You can hide away or you can face up to the reality of it."
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- Adam Lallana