Clayton Donaldson headed in the winner for the Bees in the 88th minute after County went to sleep from a corner.
A Tony Craig own-goal had put County ahead after 20 minutes before Adam Forshaw equalised when seemingly well offside before the interval.
Curle said: "We started really brightly and played the way we wanted to play but the offside goal killed us. I thought there was an infringement on Jeff Hughes before that and then the offside decision.
"I've seen it on the video and it is a yard offside. If I'd had the flag I would have put it up. Goals do change games and that was a gift of a goal that wasn't merited and wasn't earned.
"We showed our resilient side in the second half but then we feel we've been mugged off by a short corner where we didn't come alive which is something we are usually very good at."