When apologizing to your girlfriend after unintentionally hurting her, it's essential to be sincere, empathetic, and take responsibility for your actions. Here's a heartfelt apology line you could use:
"I am deeply sorry for any pain I've caused you. I never meant to hurt you, and it hurts me to know that I did. Please know that I'm truly sorry, and I take full responsibility for my actions. I value and love you so much, and I promise to learn from this and be more mindful in the future. I hope you can find it in your heart to forgive me."