How can we express regret?

That can be done by saying Sorry or by trying to make up for the mistake or harm done. 

I agree with Mr anayat answers, thanks. 

Regret means to feel sad or the feelings of unhappiness.

It can be used as a noun like: She expressed her regrets on this sad accident. 

It can also be used as a verb: She immediately regretted her words.

1. I wish I had worked harder.

2. If only I hadn't eaten so much.