Sometimes There is No Need to Explain
Someone wrong you? Or accused you of doing something that you did not do? Unless it is a legal matter, or your reputation is at stake. It is better to keep your mouth shut. There is no need to explain. It is difficult to convince the person to change their mind about you. To change their opinion about you means they have to accept that their thoughts are wrong. Not many are willing to accept being incorrect.
Moving on you can either drop this person out from your life or let your action speak for itself. But more importantly, keep your mouth shut as there is nothing to explain.