I don’t think that first statement is pointless, it just shows you have the ability to learn and to admit you’re not perfect. And regret just means you made a choice in the past, that you’d done differently being the person you are today, and you feel it would have made your life better had you choosen differently. But we all make mistakes, nobody’s perfect, I’d expect everyone to have some regrets.
A mistake is something that shouldn't have happened, regret is the same thing, with the addendum of wanting to change it or not wanting it to happen.
Time travel doesn't exist, ergo regret shouldn't exist. I think what op is saying is they don't ruminate on it and I agree, nobody should. unless you have an established pattern, then rumination is self invoked torture.
Most people I think define regret more abstractly: back in time, <X> was a _mistake_, it shouldn't have happened, _I_ shouldn't have done it that way and consequences came from it either for myself or those I love.
It seems from your response that you're ok with admitting your mistakes which - by the above definition - sounds like you feel regret.