We’re human. We all make mistakes; not one person is exempt from that statement. Sometimes we end up hurting someone we love; not acknowledging that doesn’t suddenly cause your fault to cease in existence- it’s still there. It still happened.
There’s nothing more cowardly than someone consciously making a mistake but refusing to admit their fault when confronted- this is usually where someone can, and will, lose the most respect for you. I don’t care if you messed up; have the decency to admit it.
Denial has never gotten us anywhere in life. Admitting your mistake won’t suddenly render you to be less as a human being or anything of the sort. If you really want to save any relationship (even if it’s just the one with yourself), lose the ego and be up front about it.
I’ll be the first to openly confess that I’ve hurt some of the most important people in my life this last year. I’ll be the first to admit that I have made some mistakes that drove one of my relationships down the drain. But I’ll also willingly concede to each of those in a heartbeat.
If you truly value that person and your relationship with them, you take ownership of your mistake. The straightforwardness may temporarily leave a bitter mark, but it isn’t your responsibility to make someone forgive you. If you were honest enough with them to own up to your fault, it’s their decision whether or not to accept it.
You should be able to stand up straight and say, "Yes, I made X mistake! And???." No one is innocent with their past and I'm quite certain that those who criticize you most likely have a much more grave history themselves. Let's move on with our lives.
Additionally, owning up to your mistake puts you in the driver's seat. No one can hold their accusations as any sort of power over you; you don't have to act dumbfounded and innocent. Once you yourself define the mistake, people already have one less reason to criticize you.
The strongest and best thing you can do for the sake of yourself and others is take responsibility. The same way we take pride in an award we have won or a position we hold, we must also take ownership of our mishaps. Confronting your mistake head-on will allow you to accept the error and move forward in a healthy manner.