I did a bad thing. I betrayed my girlfriend with another man.
What do you mean, you betrayed her?
I cheated on her because of my bad mood
Cheating on a partner is never smart. Not only are you hurting your potential future with them, but also their piece of mind. Talk to them, be honest about what happened.
I don't count it as cheating if we were never exclusive with each other and I've never talked to her since.
If she was your girlfriend, you had some type of relationship with her, whether it was exclusive or not. If you say you betrayed her, you should think about why you did that and use this experience to make better choices in your relationships going forward; it will lead to healthier relationships.