Whitman helps us out here by actually using the word. Remember how that spider "stood isolated" in line 2? The poet makes a big deal about how the soul is also cut-off from other objects and the outside world. A feeling of isolation might be the biggest emotional component of this poem.
In the end, the poem leaves us isolated. It brings up the possibility of connection, but, since it never happens, the overall feeling of the poem is melancholy and hopeless.