Xanathar is right: they aren't. The characters in my main campaign were all nonmagical for a long time (and even now the only spellcaster is one paladin). Everything works fine; the game is balanced around the assumption that characters don't have a lot of magic. The worst unforeseen effects happened when I did introduce a magic item which overpowered the fighter more than I'd intended.
Um, what to say specifically...
A lack of magical healing means that when combats start to go the wrong way things can get ugly. If your players aren't used to having to withdraw from fights sometimes, they may have a hard time adjusting. 5E's dying rules are forgiving enough that they don't really need magical healing to avoid frequent and ignominious death, at least not if they invest in the Medicine skill or some healer's kits, but short rests are very important. If you don't want to be too brutal, you might consider lowering the short rest time to 15 minutes so they can more plausibly back off, lick their wounds, and get back in without losing too much time.
I'd give the standard precautionary note about being careful using monsters with nonmagical damage resistances, except that I threw a wererat at my party very early on just to see what would happen, and despite being totally immune to their weapons they still took it down. (They drowned it.)