There are a couple of things to consider here. The biggest is: why did the joke fall flat?
First of all, and this is something I learned a while ago: people who try to be funny all the time are considered funny almost NONE of the time. No one takes you seriously after getting to know you, and the constant jokes wear thin.
Did the joke not make sense to your audience?
Did you joke make someone feel small?
Did you make a joke about politics to the people with the wrong viewpoint for the joke?
What was the mood of the conversation overall prior to telling a joke?
All of these are important interpersonal skills with respect to humor. Not knowing any of these, I'll make some assumptions: the joke was appropriate for the audience and the audience isn't tired of listening to constant jokes. So... how to recover as an interpersonal skill...
Usually when something I do falls flat, I'll quickly make light of it and move on. "Hey, you didn't pay admission so you don't get the good jokes." "Time to fire the writers" "Sorry for the interruption. Getting back to what were talking about..."
The main thing is to not overthink things. All that will do is make you more anxious. Even Groucho Marx had jokes fall flat; it's a part of life. Let someone else take the reins of the conversation so it doesn't appear that you are trying to hijack it, and learn from it.