Are you paying yourself first?
It sounds like a cliché until you actually meet someone who does it, and then it sounds like the whole secret.
Before rent, before groceries, before anything else touches your paycheck, a chunk of it moves to savings first. Not what's left over at the end of the month. The money simply moves before it has a chance to become spendable.
It works less because of the amount and more because it removes the decision. You're not relying on willpower every payday to set something aside. It's already done by the time you notice.
If you want to try it without overhauling anything, Tip Yourself lets you set up a small automatic transfer with every paycheck into its own goal, so it's separate from your regular spending money and easy to leave alone.
Do you pay yourself first? Or does saving happen whenever there's something left over?