Contrite: Remorseful; penitent; repentant.  

A deep feeling of guilt for wrongdoing, combined with a desire to make amends.

From Latin: contritus, “worn out, crushed, bruised” 

Synonyms: apologetic, repentant, sorry

Contrite shows up in one of the stanzas of Rudyard Kipling’s poems.

The tumult and the shouting dies;

   The Captains and the Kings depart:

Still stands Thine ancient sacrifice,

   An humble and a contrite heart.

Lord God of Hosts, be with us yet,

Lest we forget—lest we forget!

– Recessional by Rudyard Kipling