That used to be a phrase that I couldn't really comprehend, and it used to annoy me when people said it. It's like telling someone not to forget - they can try to remember, but they may very well forget. But recently, after some reading, and not a small amount of thinking, I decided not to let it bother me.
After a long time worrying about worrying, I just thought: "let it go". And I was surprised (and happy) that I felt I could. Maybe it's because I have been trying, and reading, and trying some more that I got to this stage. Sure, it might be hard putting it in to practice, but right now I've got a grin on my face. Because I won't let these little things bother me.
It will be different for different people, but I think there must be a trigger that can be fired when you get to a certain point. I don't claim to have reached enlightenment, but I will say it's a good feeling just to say:
I am how I am, and I can't change that, only become better at being myself.
Suffering is created from within, and I choose to let go of that suffering.
Things will turn out how they turn out, why worry about it?
The core truth of what I am saying is that, if you are feeling negative emotions, get to a place where you can let go of them. You could exercise rigorously to release them, but it's an exercise of the mind to let them go before they build up.