Everyone is too busy worrying about their own first impression to grade yours that hard.

Most people in a room are running their own anxious commentary and have very little attention left for yours. The awkward thing you said is competing with whatever they are worried about having said, which is why the moment you replayed for a week was forgotten by everybody else before dinner. That is not an insult. It is permission.

Go into the next new situation assuming you are not the subject. Ask people questions instead of managing yourself. The relief shows up immediately and makes you better company.