The quote that Nietzsche does from Socrates is: "Consider the consequences of the Socratic maxims: "Virtue is knowledge; all sins arise from ignorance; only the virtuous are happy"--these three basic formulations of optimism spell the death of tragedy.
Furthermore, Nietzsche adds that said "sins" that Socrates mentions are the cause of tragedy. So by simple comparison: if sins cause tragedy and Ignorance causes sins, then ignorance causes tragedy.
Another point is the "suffering" , from my point of view It is completely intrinsic of human nature. There is no suffering outside of man. In consequence, it is born from us. Natural phenomena (defining phenomena as all possible occurrences within its own axis that intersects the plane of time, creating the actual events that happens in existence) can not be considered as cause for our suffering, nor blessings from a divine entity. They are void of human meaning and only are what they are.
In that context death is just a natural phenomena and can not cause suffering, but humans beget poverty , so it could be considered a real cause. Moreover I interpret suffer as the metaphysical feeling that brings spiritual or moral pain, not of flesh.
Finally, "tragedy" defined by Nietzsche is the child begotten by Apollinian and Dionysian art.