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I may have managed a major faux pas. I used the word blithely. Is this an acceptable adverb?

i must say, I appreciate the blitheness with which you tossed out your "I used the word blithely" sentence. I should imagine you were in a blithesome mood at the time of writing it. Though you do want to be careful not to be too blitheful in your writing, or you may be accused of being overblithe.

I'm with Mark Twain:
"I am dead to adverbs; they cannot excite me. To misplace an adverb is a thing which I am able to do with frozen indifference; it can never give me a pang."

But if you must, I'll resignedly accept blithely.