You could also establish some boundaries afterwards. If it was an uncomfortable situation, have a conversation with your family about privacy. Say something like 'I know it was just an accident, but I'd really appreciate a bit more privacy in the future.' This way, you're taking steps to prevent similar situations from happening again and also making your feelings known in a respectful way. At the same time, try to move on from the incident and not let it become a big, lingering source of embarrassment.
Another way is to quickly cover up and then calmly explain what happened. For example, if your towel slipped while you were walking to your room after a shower, grab the nearest piece of clothing or towel and then say, 'Sorry about that, the towel just didn't stay put.' This shows that you are aware of the situation but are handling it maturely. Also, it can help to remind yourself that your family members are likely more concerned about your well - being than anything else. They probably just want to make sure you're okay and not be judgmental about the accidental nudity.