However, regret is less external; regret is more of being disappointed over an outcome and wishing it didn't happen this way. In america, people usually relate regret to events in our control, so we could wish we did not quit a job, wish we did not sing a song too loud, wish we drove faster, or wish we could change our past actions for a different outcome; all of those examples are examples of regret.
The key is that regret is not showing or expressing sad emotions for what has happened, that is lementing. Regret is more to do with wishing our actions in the past were different, and has no relation to the expression of those feelings.
I hope this helps! ¡Ciao!