Hi Karlo, thank you for reading.
To answer your question more specifically, I’d need more contextual information.
As a manager, you have the responsibility of your team and their mistakes.
Don’t lie and claim the mistake is yours. Instead, publicly accept responsibility for the mistake happening and lay out a plan on how you will prevent the mistake from occurring again in the future.
Nobody is perfect, and everyone makes mistakes. What’s important when mistakes are made is to figure out how to prevent them from happening again.
If the team member has a pattern of making these mistakes, then you should discuss this with the team member privately and work with them to stop the pattern.
Hope this helps,