Pools are now eight points short of safety after clinching only their second home victory of the season - their first since September - and Curle felt his players' mentality was all wrong.
Goals from Peter Hartley and James Poole earned the points as John Hughes' side won back-to-back games for the first time since September 2011.
"It's the most disappointing defeat of the season," said Curle.
"We didn't start well, very slowly and a few players thought because of Hartlepool's position in the league they could turn up and win without performing.
"Football-wise between the 18-yard boxes we did well, passed well and caused problems. Inside the 18-yard box was where we had our own problems."
Pools took a fifth-minute lead when Poole superbly controlled a cross in the penalty area and his second touch was a confident finish.
County levelled when the lively Jamal Campbell-Ryce scored a fine individual effort in the 53rd minute, cutting in from the right and shooting low into the net, but despite being in the ascendancy County succumbed to a Hartley header from close range after 69 minutes.
"It was a soft winner from our point of view, we spent a lot of time on defending and set-plays, people know their jobs," Curle said.
"Then you come to a game and they abandon their duties, top players, those at the top know their responsibility from minute one to 90.
"Lower league players tend to switch off and we have to spend more time on what we do.
"We had a two-man wall and the wrong personnel were in the wall. We went through it all on Friday, they know their jobs and then they change it on the pitch themselves."