It all depends on the situation, the cause of the problem and the extent of it. In my opinion, if the client has suffered due to the vendor mistake, best would be accept it and try to find out the next best option to overcome and dilute the damage done.
Life is really simple, but we insist on making it complicated - Confucius
Accepting the mistake is a big step and the most important one. Accept your mistake and extend your apology. Then you work on fixing the damage and if possible going an extra mile to patch up for it through compliments or discounts or if none then an assurance of not repeating the same in future. Every mistake can be taken as a learning experience. It is crucial to have a good connect with your client and so always be on your toes to maintain it.
I am open to experience what life's mystery bag holds for me
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