The phrase in question appears near the end of the poem. A miracle affects the two protagonists so intensely that they both immediately decide to abandon the world and enter the religious life.
Las vanidades del mundo
renunció allí mismo Inés,
y espantado de sí propio,
Diego Martínez también.
I'm not sure how to interpret espantado de sí propio, as this usage of de sí propio appears to be antiquated or poetic. Possibilities that occur to me are "appalled at himself," "terrified by his own actions," and "fearing for his own life."