So sorry this has happened.
I would tell the truth, but I think it's important to recognize the point made below that you don't want the kids to think it ran away because one of them pulled its tail or something like that. You also don't want them to think that, if they got lost, you wouldn't look for them.
t would open up some hope that the cat is alive but saying that some animals choose to live in the woods like their wild "cousins" (bobcats, etc.) or that there are some people who take them in to feed them if they are lost. That covers you if the cat ever comes back as well as if it doesn't ("maybe a new family is caring for it" or "maybe it's really an outside cat and went to live in the woods"). I don't think you have to go into the bad things that might have befallen it.
I agree, as said below, that the 1 year old won't get it, the 3 year old might, and the 4 year old might have the most sensitivity. However, don't be surprised if they soon move on with their lives and forget about it. That's pretty typical for those ages. Little by little, I would collect the cat's things, first to "wash them" (bowl, bed, litter box) or to "store them" (toys, other accessories). See if the kids notice over time, or if they just get used to the new situation with the lack of reminders. If the cat does return (which I hope it does), you will still have the items in storage and all ready to be put to use again.
Do use social media to post photos or descriptions, notify local shelters and animal control (hopefully the cat has tags or microchip), and let your neighbors know.