To "regret" doing something is to wish that you had not done it. It's a strong emotion, so this word should be used to describe actions that were large mistakes, not small, everyday mistakes:

I'll always regret not spending more time with my father before he passed away.

As you can see from this example, when you want to use "regret" for an action that you did not do, use the phrase "regret not ___ing".