To me, there's two different instances of being "caught bluffing"
The first - When you are called down and people see what hand you had.
The second - If you bet into a pot and someone raises you, and you have to fold. At least here, you can show that you may be a bluffer, but your opponents don't necessary know exactly what you're doing. So there's still some element of mystery as to how you were playing a specific hand/situation.
As for being embarrassed? Not at all. I try and use that situation to see what my opponent is doing, and seeing what their tendencies are, so that I can try to use that to my advantage the next time. For example, I could have run into a Calling Station who is willing to play Top Pair, any kicker, so that means that if I am in a hand with them in the future, I will need to narrow my range of "made
hands" that I will play against them.
It's key to accumulate chips in a tournament, winning the pots without premium hands. Because variance is such part of the game, if you can accumulate a good stack, you can weather those spots a little bit better than if you were basically waiting for premium hands to play.
