Your question is a bit confusing. First you ask
What single word describes how one feels when another person says something that doesn’t make sense?
but then you give the example
So and so said something so laughable I feel _____.
So first, it is good to make a distinction between making no sense (nonsensical) and laughable (so ludicrous as to be amusing, OL).
Then you say in the comments you may be looking for a feeling rather than an adjective, and a milder one at that.
I am thinking of confusion (Macmillan)
(uncountable) a feeling that you do not understand something or cannot decide what to do
- She stared at him in confusion.
Puzzlement could be considered slightly stronger, but it is not as strong as perplexity and bewilderment. It is defined as
a state of confusion because you do not understand something
- My overall feeling when reading the book was puzzlement. (Cambridge)
However, these feelings will make sense as answers to the question stated in the title of the OP. So I would re-write your sentence as:
So and so said something so nonsensical that it left me confused/puzzled.
or with a noun
So and so said something so nonsensical that it left me with a feeling of confusion/puzzlement.
Addition: There is an even milder way in which you could express this feeling:
So and so said something so laughable/nonsensical that I was left wondering/ it left me wondering.