This comedian wasn't very funny. I didn't laugh at many of his jokes.


I don't think "at" in the above is equal to its counterpart in "Don't laugh at me." If I am right, then what does "at' in the above refer to? Thanks.
You are wrong. Laugh needs a preposition and one laughs at somebody or something.
Technically, at doesn't refer to anything. at is not a referring expression. Generally, only nouns and pronouns can refer.
Nevertheless, I understand what you're saying.
Here at means 'upon hearing' or 'when I heard' or 'as I heard' or 'in reaction to' or 'as a reaction to'.
I didn't laugh upon hearing many of his jokes.