Carroll's a daft, indisciplined, lad. He's nowhere near what a good pro should be. He was getting there but had to be looked after like a spoilt child. That said, play to his strengths and provide the support and reassurances he needs and he can be destructive.
You've bought a shit winger (Downing) to provide for him and if he's not being used as the focal point of your attack then I don't see the point in playing him. You play to Suarez who can be fantastic but who is greedy and clearly has no rapport with Carroll - Toshack and Keegan it ain't.
Don't compare the price tag to the ability; you did ok out of Chelsea (we did even better). Sadly, I think you need to off load Carroll, he looks unhappy and you don't have the time to give him the time he needs.
KD left him out to dry when he took him off. That was serious bad man management and could be seen as a sign that KD has almost given up on him and certainly isn't giving him any further protection or support in the face of criticism. Left to his own devices Carroll will certainly fail.