I'd say FEMA disagrees with your assesment of their responsibilities during a disaster to the tune of about a hundred percent...
FEMA coordinates the work of federal, state, and local agencies in responding to floods, hurricanes, earthquakes, and other natural disasters.
Cops participated in looting, walked away from their post, or didn't doo much to stop the lawless thugs who run the city. Once that happened, there wasn't anything FEMA could do to stop it or bring in relief as they are not armed to control lawlessness.
Did the state place anyone in their "shelters of last resort" to assist with food and supplies? Did they deliver any food to these places when they opened them up for the citizens to take refuge from the storm? Although they knew that they had sent citizens to the Dome of hell and opened up the civic center, did they show up to speak to their constituents? Nope...they were too busy hitting all the news channels crying on TV interviews instead of minding the store. As far as they were concerned, FEMA was their to bail them out of the fix that they themselves created. Now they all stand in line to deflect responsibility, point fingers and extend their hand for federal relief. I guess you don't mind your tax dollars being misused by their inept "leaders".
Feds normally respond after the fact, just like cops. If you are being held up at gunpoint, are you going to say "Wait! I have to go call 9-11 (or FEMA)? The state didn't even utilize their own police force, the National Guard or any other assets at thier disposal.
When people are encouraged to sit on their tails and wait for help, they will always become a victim of something. People should have left before the storm and the state should have been on top of the evacuation prior to the storm but didn't want to use money from their own state to do the job that they were elected to do.