Backpropagation in multiple output neural networks
You have to pick a loss function before you can apply backpropagation or train your network.  Once you do, you can apply backpropagation.  Backpropagation doesn't tell you how to pick a loss function; that's something you have to do, based on what you're trying to achieve.

Neural networks don't have binary outputs.  Rather, they have continuous outputs.  You might want to use a logistic loss on each of the 21 outputs, and sum up those 21 losses and use that as your overall loss function.  The logistic loss is effectively a generalization of the 0-or-1 loss to the case where you have a continuous output and you want to predict either 0 or 1.