Don’t admit to errors or omissions until you consult with a proper internal team (managers, project director, financial, legal).
If you are admitting an error, make sure it is actually you or your company at fault and not the client or contractor.
However, don’t waste a lot of resources on the above if it is a small mistake on your company’s part and can be fixed easily, cheaply and with no other ramifications. (e.g. you specified table E flange on one pipe but pump to match it comes with table D flange, this may be only $100 to fix, you should make sure that as project manager you have the authority to authorize small fixes like this quickly and easily).