There is at least one other message that the poem is meant to convey. In the poem, Jonson is saying that an artist must be patient and that, if he is, he will win out in the end. So a deeper meaning to this poem (beyond the anger) is its counsel of patience and the idea that the superior man's art will be vindicated in the end.
This theme is seen most clearly in the last two stanzas. There, Jonson is telling himself to calm down and simply make great art (like those classics to which he refers). If he does that, people will eventually realize that he is a great talent and will be in awe of him.
So, beyond the anger, this is a poem about trusting in your talents and realizing that they will eventually be appreciated.