I think the only reason the sentence as-is doesn't feel quite right is grammatical. The thought makes enough sense to understand what you're trying to say without changing anything.
The issue for me is that you wouldn't "hold someone to account," you would hold someone accountable.
Between liable and responsible, I prefer the word responsible as it connotes a stronger sense of personal acceptance of the accountability we're referring to. To be liable means you may be held responsible, but it does not mean that you are responsible -it sounds more like legal jargon. For example, if I co-signed a loan with my son and he failed to pay that loan, I might be liable even though I am only indirectly responsible. I could see someone saying, "I may be liable, but it wasn't my fault!" I have more trouble with the statement, "I may have been responsible, but it wasn't my fault!"
So with that said, maybe a couple possibilities...
I am not suggesting a double-standard, I hold myself responsible to the same rules I hold others.
I accept the responsibility for my own ethics, and I hold others to the same standards accordingly.
I do not judge anyone by a harsher set of standards than I judge myself.
I'm not sure if you'll like any of those, but I hope the thoughts are helpful. Thanks for the question.