The only way to find out what you got is to see what you have now that you did not have before, and that could just be an increase in the amount of something you already had. The same is true if after beating the monster that ends a quest if you get disconnected before you have pick the card. Since the reward is determined ahead of time, when you log back on you will not go back to the pick a card, but you still got whatever you were going to get.