People make mistakes. It happens. Your job as a manager includes correcting mistakes and taking steps so that they don't happen in the future. That mean you need to tell people they make an error.

New managers often worry that they will hurt people's feeling so they put off correcting a mistake until the problem becomes major. It will be far easier to correct a wrong behavior when it first appears than after it has become a habit.

When you do have to correct someone, it is useful to know how to give negative feedback in a way that keeps people motivated instead of demoralizing them. The article How To Give Negative Feedback Properly tells you how in ten simple steps.