Is it wrong to react in this way?

Let's say you've been accused of something you never said or did by someone. I'm not gonna get into details but I've been accused of something I never said to someone. I asked my parents for advice and my mom said if you react to the situation that's going to make others think you're guilty,when really you aren't and if you know you didn't say it then you should just let the situation go. I understand how the reaction can make the situation seem compromising but to me being accused of something I didn't do by someone makes me feel like an innocent victim who went to jail on fallacious charges and being unable to prove your innocence, since it's your word against theirs. Plus,it gives me the impression that the accuser is trying to start trouble for their own sadistic purposes.I don't know about anyone else but how would you react if something like that happened to you?