Shame or dishonor cannot be covered or hidden. Death is the only release. When Hero awakens, Leonato also comments that she should not look up (line 117). Rather, Leonato is suggesting, Hero should be hanging her head in shame. Leonato then launches into his loud and angry speech in which he wishes he had never even had a child.
Toward the end of his speech or tirade, Leonato uses a metaphor to describe the extent of Hero's shame:
O she is fallen Into a pit of ink, that the wide sea
Hath drops too few to wash her clean again. (138-40)
An act of dishonor can never be removed. All of his life Leonato had acted honorably. But one act of infidelity by his daughter can destroy all of that. His life, the life he wants to live, he feels, is over. All of his honor is gone. His respected place in society is gone. So, although Leonato's speech may be shocking to audiences, the reader should understand that his irrational and angry response is a result of his fear regarding the loss of honor.