As Harry Truman would say:
The Buck Stops Here!
The sign of a good CEO is to take ownership for failures. However it is not your job to teach your CEO this, but "leading upwards" is a skill that people need.
First determine if the CEO is receptive to feedback. Do you trust the CEO to take honest critique? If not, do you have any kind of anonymous feedback system in place? Again if you don't, you might want to suggest that first.
Next know, when you can say this. If the CEO is currently blaming someone, coming out with a comment on it is not going to be received except negatively.
As with dealing with any manager, you need to focus more on solving the issue rather then explaining what they are doing wrong. The CEO is already avoiding looking bad, so pointing out is going to end any form of dialogue.
For example: Maybe suggest an internal review board to track issues, so that they can point out to their customers they have a process board to handle problems as they arise. This allows the CEO to have documented feedback of what went wrong, who was involved, and how you plan to resolve it in the future.
In that instance, you can say something like:
Rather then telling the customer X screwed up, instead you can say
'This is how we are going to make it right in the future'.
One contention point I have on your post is this:
... but usually choose a scapegoat which will be blamed publicly.
In some countries this can lead to litigation by the employee. Actually in some countries the companies can't even comment on the employee beyond "They worked here from X to Y".
If you are looking for material to read up on. I recommend "Lead your Boss: The Subtle Art of Managing Up" by John Baldoni.