I remember a really big mistake I made 20 years ago.  I won't into
details but a lot of people got the flak for my screw up.  Still, I
didn't want to leave it at that.  So I really sucked up and apologized
to those who took the fall.  I don't think I could be at peace unless
I did that.  Remembering that reminds me of the song "Sorry Seems To
Be The Hardest Word" by Elton John.

None of this world is perfect.  There are times when we really make a
big mess of things.  The worst part is when that affects a lot of
people.  When it gets to that point you have to throw pride out the
door.  You do that right thing and apologize because you know it's
your fault and that's the way to set it right.

These days people can't even bring themselves to admit their mistakes,
let alone say sorry.  Some would rather find a way to wash their off
the whole deal just to preserve their image.  Even you weasel your way
out, it will won't make things right.  It'll be an error that will
turn into a mistake that you won't fix and will haunt you day in day
out.  So even if it's hard the best way to fix it is simply say sorry.