The Collaborative International Dictionary of English v.0.48:
Regretful \Re*gret"ful\ (-f?l), a. Full of regret; indulging in regrets; repining. -- Re*gret"ful*ly, adv. [1913 Webster] re-groupWordNet (r) 3.0 (2006):
regretfully adv 1: with regret (used in polite formulas); "I must regretfully decline your kind invitation"