They know that they must be careful in pursuing anything that looks vaguely like a target, because the sentiment of the population is far more important than a small victory like that. Hence the multi-billion-dollar communications and failsafes chain described in this article. This is a key concept that seems to be going over people's heads in this thread. Yes, it failed in this case and in many others. But the very fact that it exists at all and is sophisticated as it is should be a clue as to the lessons learned. The military is achieving far more value with far less collateral damage. Contrast this with the Soviet's preferred method of waging war against the Afghani Mujahideen, which was to kill every living thing and totally and utterly raze every structure in the direction from which they were shot at from.
So again, can you conceive a better alternative for dealing with reality as it is now? Time travel is not possible, answers like "don't invade other countries" are pretty worthless. Nobody wants this war(well, nobody with a soul and a modicum of compassion), but it is what it is, and as far I know, it's the best solution to minimize civilian deaths.