Honestly admitting that you made a mistake never hurts and you ought to do it whether he comes back to you or not. Few people think about the hurt that they cause to another person when they break up. When you are close to someone and they tell you that you are not adequate, it forms a deep wound.
But whether he wants to return to dating someone who is willing to break a relationship over petty things is really up to him. You can let him know you are available, but you should show him enough respect to allow him to make his own decision -- and then to respect that decision, whether you like it or not.
Many thanks for your response. I sent him an apology today and I feel some weight off my shoulder.

