1
Regretfully, + [clause]
句首用作评注性状语，相当于“I regret to say that...”。
Regretfully, we cannot accept your offer.
很遗憾，我们无法接受您的提议。
遗憾地；抱歉地
先理解核心含义，再看它在真实句子里的用法。
遗憾地；抱歉地
in a way that shows regret; used in polite expressions
Regretfully, we cannot accept your offer.
很遗憾，我们无法接受您的提议。
遗憾地；后悔地。
In a regretful manner, with regret.
Regretfully, we cannot accept your suggestion.
很遗憾，我们无法接受你的建议。
She shook her head regretfully when she heard the news.
她听到消息后遗憾地摇了摇头。
Regretfully, the store will be closed all day tomorrow.
很遗憾，这家店明天全天关门。
句首用作评注性状语，相当于“I regret to say that...”。
Regretfully, we cannot accept your offer.
很遗憾，我们无法接受您的提议。
修饰动作，表示带着遗憾或歉意做某事。
He shook his head regretfully.
他懊悔地摇了摇头。
Not this
She looked at the letter regretful.
Use this
She looked at the letter regretfully.
这里需要修饰动词 looked，表示带着懊悔地看信，所以应用副词 regretfully；regretful 是形容词，不能修饰动词。
Not this
Regretfully, the shop was already closed.
Use this
Regrettably, the shop was already closed.
regretfully 意为“懊悔地，抱歉地”，强调人的感受；表示“遗憾的是，不幸的是”这一评注性含义时应用 regrettably，两者不可混用。
Focus on the distinctions below. Other candidates are kept compact until a reliable usage note is available.
遗憾地婉拒
She regretfully declined the offer.
她遗憾地婉拒了那个提议。
遗憾地通知
We regretfully inform you that the event has been cancelled.
我们遗憾地通知您，活动已取消。
遗憾地承认
He regretfully admitted that he had forgotten the appointment.
他遗憾地承认自己忘了约会。
遗憾地接受
I regretfully accept your resignation.
我遗憾地接受你的辞呈。
“很遗憾，是的。”——出自电影《公主新娘》：行刑者被问“会不会很疼？”时如此回答。
Regretfully, I must decline your invitation because I already have plans.
很遗憾，我必须拒绝你的邀请，因为我已经有安排了。
Use regretfully naturally, then get feedback on meaning, tone, grammar, and phrasing.
Revisit a common error or keep this word in your review list.
regret(后悔) + fully(满满地) → 满满地后悔，懊悔地道歉。
语域：formal 常见场景：formal letters、official announcements、polite refusals regretfully 通常用于正式场合，多出现在正式信函、公告或礼貌的拒绝中，表达遗憾或抱歉。口语中较少用，比较书面化。
regretfully 是副词，常与 regretful（形容词）混淆；表示“遗憾地、抱歉地”，多用于礼貌用语。
Dictionary facts from ECDICT, WIKTIONARY.