Well, seeing as how anyone in a decision-making capacity has been appointed by the US (sorry, sorry, "the Coalition"), yes you are responsible. No one so much as takes a piss without the CPA's say so, and I think that the Iraqi people recongize their "government" for what it is; a puppet regime.
Now, the big mistake was pissing of Muqtada al Sadr. It is estimated that anywhere from one third to one half of all Iraqis support him, so trying to shut him down might not be the wisest thing to do. He's got his militias up in arms all over Iraq.
If the Shia ever come to stand united against the US, its going to get very bloody very quickly. And this guy, he seems likely to be the man to make it happen.