The Royals were well beaten at the Madejski Stadium, making it five matches without a win at home.
"We were playing a team well below us in the league and yet we failed to capitalise on that. Across the team, we were poor. We were just not good enough," Adkins told Sky Sports News.
"We're still in the playoff race but we were very poor this evening. No one can hide away from that fact."
Reading are sixth, while Barnsley are now three points behind Charlton Athletic, who are 21st.