I Blabbed My Student's Secret in Class

Yesterday, I was leading a quiet discussion about personal goals and dreams. One of my students, Jamie, shared a big secret, something that they've been struggling with at home and were afraid to tell anyone else. After class ended, another student, Sarah, came up to me with her own problem and started talking. In the middle of our conversation, I accidentally mentioned Jamie's secret without even realizing it! Now, I'm beating myself up over this, I know how much trust Jamie put in me. Is what happened normal? Should I just apologize sincerely or should I do more? What would you do if you were in my shoes?