When you are in an in the midst of an embarrassing moment, you can imagine that you are the only person on earth and hope that the earth opens up and swallows you so that you may escape the mixed emotions that you would be experiencing. Everyone gets embarrassed and so it isn't something to be disturbed about, because it actually serves a purpose. It helps one discover who you can trust and build further relationship with. It can be a bridge to connect you to other if you handle it well. One of the things that you could do is take it in stride.
You are not Dangote. You can laugh it off. Several research indicate that laughter is as good as medicine. It is a smart way to overcome anxiety. Laugh at yourself and the situation that incites the feelings of embarrassment. It gives room for others to laugh with you instead of at you. It can be an icebreaker and help you meet and make new friends.
Be honest about how you feel:
Say out loud, 'this is so embarrassing’. Embrace and own the moment. Share the moment with the witnesses to the embarrassing moment. Talk about it. Smile and let it go. Don't rehearse it and don't replay it in your mind. It happened and you are choosing to move on from that point.
If you farted for example, you can explain how that you had eggs at dinner or at breakfast before going to work/school and why you think it happened. Be understanding and kind to yourself.
Ask for help and appreciate it when offered:
If you spilled coffee over your shirt, collect the paper napkins that are passed to you and say thank you. If you fell, receive assistance from whomever is helping you up. Be vocal about the thanks, don't murmur, it will help distract you from the embarrassing incident.