Sky Sports pundit Carragher was speaking after criticising the Ivorian during his Monday Night Football analysis.
Kone was at fault for the first goal in the 4-1 defeat against Arsenal on Saturday, and has looked a shadow of the player who performed so well in Sunderland's successful fight against relegation last season.
The Black Cats face another battle for survival after picking up just two points from their first 10 games, and Carragher says the squad of players is poorer than the Aston Villa side which dropped into the Championship last season.
“I said this about Aston Villa last season but I think Aston Villa had more quality than this Sunderland team. I just think there was a real bad attitude going through that Aston Villa team,” he said.
“I don’t see a bad attitude at Sunderland. I see a really poor group of players who would struggle in the Championship.
“But there’s one player whose attitude on the pitch this season has been nowhere near acceptable and I think that’s Kone at the back.
“I think he was a man mountain last season, him and Defoe. They virtually kept them up. But he’s nowhere near where he needs to be and he’s causing Sunderland no end of problems.
“(It was a) lazy performance against Arsenal. (He was) not interested in doing his job properly.”
Kone was subject of a £18million bid from Everton in the summer, but Sunderland blocked the move and handed the defender a new, improved contract.