We regret to inform you that you are being furloughed indefinitely.

我们遗憾地通知你：你被无限期地停职了。

《柯林斯英汉双解大词典》

We regret to inform you that your application has not been successful.

我们很遗憾地通知您，您的申请未通过。

《牛津词典》

Before you get carried away with your little scene, Miss Wenzmore, I regret to have to tell you again that we are not planning to go into television.

在你被你的小场景冲昏头脑之前，温兹摩尔小姐，我很遗憾地再次告诉你，我们不打算进入电视行业。

youdao

Sometimes,people say something to a friend or family member that they later regret because it hurts that person's feelings.

VOA: special.2010.06.20

Because you will come to regret it if you don't do it. But we're not going to grade it.

但是我们不会对此计分,因为不计分所以让你们。

麻省理工公开课 - 计算机科学及编程导论课程节选

This is great when you want to express regret for something that you perhaps did not do.

当你想表达对一些过去没做成的事情感到后悔时，你可以使用这个句型。

I should have 课堂 - SpeakingMax英语口语达人

"I regret to this day not calling a lawyer before leaving the (United States), " she added.

CNN: Legal immigrants: What about us?

I'm grateful for this opportunity, although it is -- comes with deep regret to be before you.

CNN

"We really regret to see Ginny decide to do this, " he told CNN.

CNN: Head of agency that runs Logan Airport resigns