regret

regret, repent

这两个动词均有“后悔”之意。
regret: 指对已发生或未发生的事或行为表示后悔或婉惜。
repent: 正式用词，语气较强，指对自己所做的错事或不该做的事感到深切的悔恨。

名词 regret:

1. sadness associated with some wrong done or some disappointment
   同义词：sorrow, rue, ruefulness

动词 regret:

1. feel remorse for; feel sorry for; be contrite about
   同义词：repent, rue
2. feel sad about the loss or absence of
3. decline formally or politely
4. be sorry

1. We regret that we are unable to reconsider your case.
   我们很遗憾无法再考虑你的情况。
2. She immediately regretted her decision.
   她做出决定后立即感到后悔。
3. We informed her with regret of our decision.
   我们遗憾地把我们的决定通知她。

re.gret

v.（动词）
re.gret.ted,re.gret.ting,re.grets
v.tr.（及物动词）
To feel sorry, disappointed, or distressed about.
后悔，惋惜：对…而感到惋惜、失望或苦恼
To remember with a feeling of loss or sorrow; mourn.
哀伤，悲叹：带着失落感或悲伤回忆；痛惜
v.intr.（不及物动词）
To feel regret.
后悔：感到后悔
n.（名词）
A sense of loss and longing for someone or something gone.
悲痛：失落感和思念失去的某人或某物的感觉
A feeling of disappointment or distress about something that one wishes could be different.
悔意：对希望能不同的东西的失望或苦恼的感觉
regrets A courteous expression of regret, especially at having to decline an invitation.
regrets 遗憾，惋惜：有礼貌地表达遗憾，尤其是对不得不拒绝的一个邀请而感到遗憾

来源：
Middle English regretten [to lament]
中古英语 regretten [悲伤]
from Old French regreter
源自 古法语 regreter
re- [re-]
re- [前缀，表.又，再.]
-greter [to weep] [perhaps of Germanic origin]
-greter [哭泣] [可能源于日耳曼语]

【引伸】
regret.ter
n.（名词）
<参考词汇><同义词>regret,sorrow,grief,anguish,woe,heartache,heartbreakAll of these nouns denote mental distress.
所有这些名词都指精神上的痛苦。
Regret has the broadest range,from mere disappointment to a painful sense of loss, dissatisfaction, self-reproach, or longing,as over something lost, gone, done, or left undone:
Regret 的含义最广，从简单的失望到痛苦的失落感、不满、自责或渴望，如对失去、离开、完成或剩下未完成的事感到痛苦：
例句：
He had hoped that our policy of not dealing with terrorists would be an example to other countries but soon realized, to his regret, that we didn`t practice what we preached.
他曾经希望我们不和恐怖分子打交道的政策能成为其他国家的榜样，但是很快就遗憾地认识到我们并不实施我们所宣扬的政策。

例句：
She looked back with regret on the pain she had caused her family.
她痛心地回顾她给她的家庭所带来的痛苦。

Sorrow connotes sadness caused by misfortune, affliction, or loss;it can also imply contrition:
Sorrow 的含义是由不幸、苦难或失落而造成的悲伤；也暗示悔恨：
例句：
.sorrow for his women, for his kinfolk, for his children, who needed his protection, and whom he could not protect. (James Baldwin).
.为他的女人、亲戚、孩子这些需要他的保护而他又保护不了的人而感到悲伤. （詹姆士·鲍德金）。

Grief is deep, acute personal sorrow,as that arising from irreplaceable loss:
Grief 是深切、尖锐的个人痛苦，如由于不能弥补的丧失而造成的痛苦：
例句：
.Grief fills the room up of my absent child,/Lies in his bed, walks up and down with me. (Shakespeare).
.失去孩子的痛苦弥漫了整个房间/充满了他的床上，随我来回走动. （莎士比亚）。

Anguish implies agonizing, excruciating mental pain:
Anguish 指令人难以忍受、折磨人的精神痛苦：
例句：
.I pray that our heavenly Father may assuage the anguish of your bereavement. (Abraham Lincoln).
.我祈祷我们的上帝能缓和你们丧失亲人的痛苦. （亚伯拉罕·林肯）。

Woe is intense, often prolonged wretchedness or misery:
Woe 是剧烈、经常是漫长的不幸或悲惨：
例句：
.the deep, unutterable woe/Which none save exiles feel. (W.E. Aytoun).
.深切的，不能言传的痛苦/没有别人，只有亡命他乡者才能感觉到. (W·E·艾顿）。

Heartache most often applies to sustained private sorrow:
Heartache 通常指持久的内心痛苦：
例句：
The child`s devastating problems are a source of untold heartache to the parents.
孩子灾难性的问题是父母无数的痛苦的源泉。

Heartbreak is overwhelming grief:
Heartbreak 是极度的悲伤：
例句：
.Better a little chiding than a great deal of heartbreak. (Shakespeare).
.宁愿要一些责骂，也不要大量的悲伤. （莎士比亚）。