The duo's error-strewn displays recently have seen City stumble.
Toure, 28, told mcfc.co.uk: "We have to improve our defending. We have top-class players and we have to take responsibility at the back.
"As defenders we need to work like brothers.
"We feel vulnerable at the moment, which isn't good. We have to be stronger. It's difficult to take. In fact, it's killing me. But as captain of this team I will take the responsibility."