Its generally seen as very disrespectful and disloyal to tell someone else's secret without their permission and so its natural to feel bad after doing so, especially if the person you told the secret to is a mutual friend
Consider the statement "I accidentally told my best friend's secret to a mutual friend". Based on this "I feel terrible that I was careless enough to accidentally tell my best friend's secret to a mutual friend" a true statement? Yes, no, or I don't know?