Source : Webster's Revised Unabridged Dictionary (1913)

Regretful \Re*gret"ful\ (-f?l), a.
   Full of regret; indulging in regrets; repining. --
   {Re*gret"ful*ly}, adv.

Source : WordNet®

regretfully
     adv : with regret (used in polite formulas); "I must regretfully
           decline your kind invitation"