The only player that I can say has looked to me to be disinterested at times is Bacuna, but then that seems to be his natural demeanor - he's often looked lethargic from day one.
I genuinely don't believe any of these players either don't care or are not trying. Instead, I think the side simply isn't good enough. The midfield is badly lacking in quality, there isn't nearly enough width or creativity, the defence is often all over the shop and several of the players are just not up to this level no matter how hard they try.
I believe City will avoid relegation due to the various problems at the four other clubs who are in the mix, but the biggest worry going forward is that this manager really does appear to be out of his depth. Given the number of players who are out of contract in the summer and the amount of wheeling and dealing that will need to be done, that's a huge concern.