I am new to MtG, for this, I started playing the old PC game "Magic 2014 - Duels of the Planeswalkers", in order to get familiar with the game, and I modified my mono black deck as a zombie/undying deck.
Playing the campaign, I faced a Slivers deck, where my opponent had 3 1/1 Sliver tokens, and I had Black Cat under the effects of Lord of the Undead and Undead Warchief making the cat a 4/3.
I decided to attack with Black Cat and these 3 tokens blocked my attack, each of these tokens dealt 1 damage each, killing my Black Cat, but these 3 tokens didn't die... why? I was expecting to kill the tokens, they attack my card (3 attack to me) and my card deals 3 attack to them which is sufficient to kill them all. Do I have it wrong how blocking works in MtG?