Don't assume your children feel the way you do. Allow them time to express feelings in various ways. Young children who haven't yet developed strong verbal abilities tend to express grief physically and through play. So listen and watch for clues. Keep it simple.
Direct language works best.
Use the words died and death in your explanations. Of course you'll need to tailor your words to each child's age and emotional development. Don't hide your grief. It's appropriate to show your own feelings, but verbalize them too, so your children don't misinterpret intense sadness as anger, for example. Your children will take cues from you.