Another way to look at it is …….that there are no consequences if you miss on the practice green, so you are relaxed and just rolling the ball into the hole.
On the course, there are of course consequences (or so we believe), so tension and stress come into the equation.
Given the above premise, there are then of course, only two options to choose from.
1. You can play your golf without consequences .... eg, don't care at all, if they do drop or they don't, thereby replicating your practice golf.
2. Practice with consequences.
To do that, here's a suggestion.
On your way to the practice green, fill your left pocket with coins or notes. For every putt that you hole, a coin or note gets to stay in your left pocket. For every putt that you miss, transfer a coin or note into your right pocket.
At the end of your practice session, reach into your right pocket, and whatever coins or notes are there, then throw them away.
Do that a few times and you may get used to putting under pressure.
Just my thoughts …..