So please it’s not too late to stop spending on things that doesn’t really matter, so basically the money you saved today could literally save you tomorrow.
But will you keep saving when there's a better way for you to secure tomorrow which is by investing? Investing offers a better option to me than saving because in saving your money may be losing value due to inflation but when it comes to investing the money is building value against tomorrow. Do not save without investing. If you want to have things easier for you tomorrow then it is better to make sacrifices today to make good investments that will be profitable for tomorrow.
From what Op has addressed about savings he didn't seem to despite investment but only laying emphasis on the importance of savings and how it could salvage us in an emergency times. Investment is indispensable in this harsh economy where inflation is ravaging and devaluing the proceeds of our efforts but investment can't plays a different role as it can't meet emergency demand but savings can be taken out immediately to solve emergencies as immediately they arise.
So I'll suggest, if the size of your income isn't efficient to start investing from it based on your responsibilities then make room for savings and save as much possible in the little ways you can. If you fall to invest don't fail to save, if possible don't fail to key into the two areas.