@gyi3 personally, as a man, I wouldn't want you to fake it.
I can completely identify with your DH (been there, done that, got the T shirt..). It's really good that you have recognised it, and are concerned by it.
You don't say how old you are, but I believe a lack of libido can be linked to the menopause.
Alternatively, if your DC is very young (under @18 months), then it could just be your body telling you you aren't ready to concieve another child yet (even if you weren't planning to!) or you may just be worn out from the demands of being a mum.
You could consider consulting your GP (if you can get an appointment!).
Whatever you decide to do, I'd definitely sit down with your DH and talk to him, if you haven't already.
This sort of issue can soon turn a relationship toxic, so the sooner you can assure him that it's not him, that you still love him, (huge assumptions here on my part), and that it's something you are working on, he (hopefully) should be receptive, and understanding.
I'm loath to suggest this, as I'll probably be flamed to hell and back, but you could consider occasionally offering him a helping hand, as it were... It would show him that you still want to be intimate with him, despite you not feeling it..
You may also find that it starts turning you on!
Good luck, it's a horrible position to be in.