In a way that shows sadness or disappointment about something that happened or must happen.
From 'regret' (from Old French 'regretter,' possibly related to 'greter' meaning 'to grieve'), combined with '-ful' and '-ly' to form an adverb describing how someone expresses regret.
The fact that 'regretfully' exists as its own word shows how deeply humans feel regret—we needed a special way to describe the tone of voice and body language someone uses when they're disappointed. It's one of the most human emotions and languages naturally evolved a word for expressing it.
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