The gross misrepresentations of history in Cosmos illustrate his disinterest in accurary about anything outside his field. Other than that, his explicit comments on the humanities have mostly been targetted at philosophy. Here are a couple:
Up until the early twentieth century, philosophers had material contributions to make to the physical sciences. Pretty much after quantum mechanics, remember, the philosopher is the would-be scientist but without a laboratory, right? And so what happens is, the 1920s come in, we learn about the expanding universe in the same decade as we learn about quantum physics, each of which falls so far out of what you can deduce from your armchair that the whole community of philosophers that previously had added materially to the thinking of the physical scientists was rendered essentially obsolete, at that point, and I have yet to see a contribution -- this will get me in trouble with all manner of philosophers -- but call me later and correct me if you think I've missed somebody here. But, philosophy has basically parted ways from the frontier of the physical sciences, when there was a day when they were one and the same. Isaac Newton was a natural philosopher: the word physicist didn't even exist in any important way back then. So, I'm disappointed because there is a lot of brainpower there, that might have otherwise contributed mightily, but today simply does not.
-- NDT in conversation with Richard Dawkins
Interviewer 1: Philosophy was my major, and I remember --
NDT: That can really mess you up.
[. . .]
Interviewer 1: It's when it starts crossing over with math and science, and you're solving -- if you -- if you have to solve an argument using math -- you know, ps and qs and whatnot, and then -- but the idea that the philosophy of science and math is like, well, why is a yard a yard? And what makes this this? You know, it's -- I, I always felt like maybe there was a little too much question-asking in philosophy?
NDT: I agree.
[. . .]
Interviewer 2: I think a healthy balance of both [science and philosophy of science] is good, a healthy balance of both is good.
NDT: Well, I'm still worried even about a healthy balance. Yeah, if you are distracted by your questions so that you can't move forward, you're not being a productive contributor to our understanding of the natural world. And so the scientist knows when the question, "What is the sound of one hand clapping?" is a pointless delay in your progress.
[. . .]
Interviewer 1: Philosophy was a good major for comedy, I think, because it does get you to ask a lot of ridiculous questions about things.
NDT: No, you need people to laugh at your ridiculous questions.
-- Nerdist podcast, March 2014 (20:19 onwards)
Between them these snippets illustrate that:
Here's one further snippet that's a bit more broadly targetted:
I can tell you, for what it's worth, that scientists by and large are actually quite knowledgeable in areas outside science. If you go to the home of most scientists, there'll be Bach and Beethoven and Shakespeare on the shelves. And they might not know as much as the literary scholar, but one thing I think that as a nation we should be embarrassed by is that the scientists -- you can do this experiment yourself, I've done the experiment -- the scientists, by and large, know more liberal arts than the science that is known by liberal artists.
-- NDT speaking at the World Science Festival, 2010
This one also suggests that his comments are born more of ignorance than a premeditated ideology. I suppose he'd admit, if you put it to him, that research in the humanities doesn't consist of listening to European classical music and reading Shakespeare for pleasure. But I'm not actually sure. Or maybe he'd say that he draws a distinction between humanities and liberal arts degrees (which humanities scholars can also be pretty scornful of, by the way).