I actually think America handled 9/11 rather well. The immediate response, at least.
Considering the scale of the attack, 3,000 deaths was lower than it could have been. There was panic in the streets, but not rioting. Lots of firefighters and first responders went unecessarily to their deaths, a lot of people got sick from the debris in the air, but it’s not really clear what precautions people could have known to take. As @Cruiser said, there is only a limited amount of things a top-down government can do in such a crisis; though I think it helps if the people in charge of that apparatus are actually experienced in disaster management (unlike Brown during Katrina).
We also succeeded in not retaliating against the Muslims by nuking Mecca, as I remember many people saying we should do.
But in the long term, we failed in many ways. We failed to provide health care for the first responders who risked their lives. We used fear of 9/11 as a pretext to go to war in Iraq, as a pretext for torturing prisoners of war.
In the long term, I think it is a statistical inevitability that America will suffer another terrorist attack; possibly even a nuclear attack. We are, for better or worse, the world’s hegemon/empire; there are a lot of unbalanced individuals and cult groups that absolutely hate us, and it is becoming easier and easier for a few individuals to kill massive numbers of people. Maybe we can change our foreign policy so that fewer unbalanced individuals want to blow themselves up to kill us. Or maybe we can move more towards a hypersecure police state. But ultimately, neither of these changes is going to happen “all the way,” such that there is no longer any threat from terrorists whatsoever.
What we really need is some perspective. 3,000 people were killed on 9/11. 17,000 additional people are murdered each year. Now, you can argue that we could save those lives through any number of measures: through strict gun control, through better education and opportunities, through tougher crime laws, through moving towards a police state. Maybe you could reduce the rate. But the rate is never going to be zero, because there are always going to be psychopaths and there is always going to be some way of killing people.
This doesn’t mean we should sit on our feet and accept it, but it does mean that we should stop thinking about “defending” ourselves from terrorists in military terms, as if they are MIGs invading our airspace, and start approaching terrorism in terms of crime.