According to Julie Winkle Giulioni, two of the most powerful things you can say to employees that demonstrate your candor are:
“I was wrong. When supervisors share their vulnerability and admit mistakes, it has a powerful effect on their employees. Rather than undermining respect or esteem, it actually inspires confidence. It creates an environment in which failure isn’t fatal, experimentation is encouraged, and problems are openly addressed, helping others learn and grow.
“I’m sorry. Apologies are powerful… for both those on the giving and the receiving end. Recognizing a problem, misstep, or misunderstanding and correcting it is not for the faint of heart. It’s hard for many… which makes it all the more impactful. Apologizing when appropriate communicates your humanity and a sincere commitment to your relationship with others.”
Neither “I was wrong” nor “I’m sorry” make you appear weak or less authentic. On the contrary, your calm, factual accountability engenders respect, and encourages your employees to do the same.