meaning of "fallen little short of a mother in affection" in Jane Austen's Emma, Chapter I

Solution 1:

The meaning of fall short is more like not quite reaching. For example, if you throw a ball and it falls short then it doesn't go as far as you intended to throw it, it does not reach its target.

From this you can see that fall short might have a negative meaning if someone's behaviour falls short of what is expected of them.

However, in your quotation the expression is qualified by little. Austen means that the governess had fallen short of being a real mother by such a small amount that she had been almost as good as a real mother

Solution 2:

But it doesn't say "had fallen short". It says "had fallen little short":

small in amount or number

It's a litotes.