Her head was bowed, as if in regret or shame.

她微微低着头，似乎在羞愧或后悔着什么。

youdao

Ambitious people, although often regret, but not regret in the depression, and probe in regret.

有抱负的人，虽然也常常后悔，但不在后悔中消沉，而在后悔中求索。

youdao

This report was published in good faith but we regret any confusion which may have been caused.

发表这份报告出自诚意，但是我们对可能引发的任何混乱而感到遗憾。

《柯林斯英汉双解大词典》

In New York, Iranian President Mahmoud Ahmadinejad said President Obama will regret saying that Iran has been building a secret facility.

VOA: special.2009.09.26

In the next example you can use "I'm sorry" not to express regret for your personal fault.

下一个例句中，“I'm sorry”的使用并不是用来表达对个人过失的抱歉。

I'm sorry 课堂 - SpeakingMax英语口语达人

The president said he had considerable regret in accepting the resignation of "one of our nation's finest soldiers."

VOA: special.2010.06.26

LeBron James does not appear to be a man saturated in regret.

WSJ: Jason Gay: What Linsanity Says About New York

Cerf, who helped design the first protocols that allowed information to be sent across computer networks in the late 1970s, expressed regret in a speech Tuesday that he hadn't designed the Internet to be a safer, more regulated system.

FORBES: Made For Hacking

Mr Checchi's millions did have at least one effect: they persuaded the most formidable Democrat, Dianne Feinstein, not to run in the first place (a decision she is now said to regret in light of the result).

ECONOMIST: A steady lot, the Californians