After many years in account management, I have learned clients cringe when you tell them bad news.  The best way to handle this is to prepare yourself with a process to deliver bad news.  I developed a process that worked. The process kept superiors and clients informed and abreast of what was happening.   

First, you must put everything you are working on aside.  Develop your strategy for the mistake at hand.  Address all the concerns in detail.  Some questions to ask yourself.  Will delivery dates change?  Will the price change?  Will your final product look different.  Write your plan to address all the questions.  Present to your superiors and get their buyin.  

Talk to the client immediately, preferably in person.  The next option is to have a phone call with the client.  Once the client is notified of the situation, it is imperative to keep them informed until the situation is completely resolved.

Being available, open and honest with your client will have a tremendous effect on their future business with you.