Source : Webster's Revised Unabridged Dictionary (1913)

Deservedly \De*serv"ed*ly\ (-z[~e]rv"[e^]d*l>ycr/), adv.
   According to desert (whether good or evil); justly.

Source : WordNet®

deservedly
     adv : as deserved; "he chalked up two goals which deservedly gave
           Bolton their second victory of the season" [ant: {undeservedly}]