Marlon Harewood opened the scoring for Barnsley, but Greg Halford, Simon Cox, Chris Cohen and Jermaine Jenas replied with goals for Forest and Hill admitted his team struggled to compete with Forest's proven talent.
"We're in the same position as we were yesterday - trying to punch above our weight," he said.
"Take the emotion out of it, you can't give a good team bad goals, and that's what we've done today.
"The players are responsible for the decisions they make on the pitch and they made bad decisions today and it's cost us the game. We got a one-goal advantage and then we imploded.
"But I haven't got the same agenda as Nottingham Forest.
"On paper, it's not a real match-up when you look at Nottingham Forest compared to ourselves. I'll admit it, they're a better side than us.
"You look at the likes of (Billy) Sharp, (Simon) Cox, (Jermaine) Jenas - I mean come on!"
Hill felt the hosts' poor defending allowed Forest to regain a foothold in the match.
"You don't see it coming. They're an excellent side but we have helped them today and hindered our own progress," he said.
"It's difficult to digest at this moment, but basically bad individual mistakes have cost us."