Saving doesn't only mean you hold your money in the bank. You can save money in any other places, including at home. You just don't spend them and don't invest in anything not highly liquid, and in case of OP not stable. In case of OP it is to have some stash for unexpected expenses.
Of course it is good to have some amount just in case, but if to save money for it involves present cuts in important and necessary expenditures, it is a waste, because if you really need something your needs won't disappear and inflation can cut part of your savings. Moreover some needs can demand more investment with time. So it is important to manage your finance wisely and not to be too obsessed with saving.