What does Bloomberg's 'concessionary tone' mean?

Looking at the definition of concessionary, and in the context of the NYTime article, I would pick:

the act or an instance of conceding (as by granting something as a right, accepting something as true, or acknowledging defeat)

the admitting of a point claimed in argument

(Here the point being that they have failed to response adequately to the crisis)

This is in line with this other extract:

At each stop, Mr. Bloomberg admitted that his administration had failed to respond adequately to the storm that struck on Sunday, and everywhere he went, officials heaped more criticism upon him.

Even though he is willing to acknowledge the mistakes made (hence then 'concessionary tone'), the response of the public isn't less but even more criticism.