Yes you're right. Carbs are part of what helps to you poo properly. The physiology of it is complicated so I'll spare you but low carb diets will make you more prone to constipation.
I had a particularly nasty episode last year when I really reduced my carbs and needed suppositories etc to solve it. I'm back low carb-ing again but I'm having smaller amounts and intermittently using senna to help keep things moving. Seems to be working so far. Good luck x