Laughing at yourself in front of the team makes you safer to follow, not weaker.

Perfection is uncomfortable to be around, because a leader who cannot be wrong makes everybody else careful. Laughing at your own mistake tells the room that errors are survivable here, which is exactly what people need to believe before they will risk anything in front of you. It reads as steadiness rather than weakness.

Next time you get something wrong in front of the group, name it lightly and carry on instead of explaining it away. Watch who relaxes. Those are the people who were holding something back.