When an employee does work, I have a simple rule - if the work is great, they get the credit. If not great, the manager takes the blame. The caveat to that rule is that is the public message, for outside the team. Inside the team, and with the individual employee, the message is slightly different.
You want the employee to take ownership of the work. You want them to know that the final product is a reflection on their skill and abilities - so they should take it seriously. Let the employee know that the final product is how you are going to judge them. It isn't a "final" judgement, because you know that no one is one project, they are a body of work. You also know that they are expected to get better, not be perfect.
The reason you send a different message outside the team is twofold:
You want to protect the employee from unnecessary criticism. As manager, you job is to make sure they are in the position to do their best, and if they are worried about the outside pressure, they won't.
It allows the employee to develop and build trust in you. Engaged employees feel support from their manager, not the fear that they won't be protected from other people outside the team.
It is your job to hold the people on your team accountable. This isn't about being nice or protective. In private, you point out the mistakes and help them grow. In public, you shelter them so they can succeed.