I don't think anyone can live a life without "mistakes". They are not mistakes, they are learning experiences.
There are plenty of reasons of saying or not saying "Sorry". As long as you learn... you grow. If you hurt others, you can apologize, but it does not change the fact that you did what you did.
In most cases, "sorry" is an automated response not related to any thinking whatsoever.
To realize you have to think, whether you say "sorry" or you don't, whether you regret your choices, your actions.
But regrets are futile. Just learn and move on.