If we define "tone" as the attitude of the poem towards its subject matter, I think that Parker's tone is one of fear towards the normalizing effects of society.  Parker presents a tone that shows fear towards what a society can do to the unique individuality of a living being.  The rose's beauty is dismissed by society as something replaceable.  The bird that died is discarded in the same way.  There is a fearful tone in how Parker describes the way and relative ease with which society is able to discard individual sadness and the death of the unique experience.  It is for this reason that the speaker, presumably Parker herself, flees from the clutches of a social order.  She understands that the manner in which society functions is one in which individuals are discarded.  The tone is one in which society is seen as an encroaching element that does not pay much attention to the experiences of the individual.  Rather, the tone reflects how rationalization is a part of the process.  Rationalization is the way in which society normalizes pain and hurt. This tone is why the speaker at the end does not which to stick around in such a condition and "does not wait" to flee.