The idiomatic expression is "fell flat", to mean that nobody laughed at it.
Oh man I told this joke last night and it totally fell flat.
If a professional comedian repeatedly "falls flat" during his "set", we say he "bombed", or he "died on stage".
There are various ways to describe your reaction to telling a joke that falls flat, but you might say something like, "I felt like an ass." Other options:
I told this joke but totally blew the punchline and no one laughed.
I told this joke and no one laughed. I just wanted to go crawl under a table (I was really embarrassed).
I told this joke and when I got to the end no one laughed. I guess they all have sticks up their butts (lack a sense of humor).
[Disclaimer] The expression "I felt like an ass" may not be appropriate in "polite" company. A more socially acceptable expression might be "I felt like a fool", or "I felt like an idiot".
The expression "they must have sticks up their butts" is a graphic metaphor that is definitely not appropriate everywhere. Instead you could say something like,
Their sense of humor must be broken.
or use an even more playful and evocative expression like,
They wouldn't know a good joke if it mugged them in an alley and stole their wallets.