Missing on the “amateur side” is common for, well, amateurs. When putting, the better putters always miss on the high side and miss long. This is especially important on bentgrass greens that break quite a bit. On championship bermuda, putts generally go straight and hold up with the grain, but fast championship bermuda greens can leave many amateurs on the low side of the hole.
So, why are your putts always short and below the hole? The biggest problem I see with most amateurs is they do not hit putts with conviction. They have a long putting backstroke and decelerate as they get to impact. If you decelerate with any swing in golf you are going to lose the line and distance. This is true with drivers, irons, wedges and the putter.
If you struggling getting the ball to the hole when putting, take a shorter back stroke and a more firm forward stroke. If you can come through more firm than you go back, you will end up being a much better putter.
I would also suggest always trying to take the line above the hole. There is nothing worse than missing putt after putt on the low side. If you miss a putt on the high side, it still has a chance to drop in. If you miss a putt on the low side, there is no chance it is going to go in.
So, take a shorter back stroke, come through with conviction and take the high side. This will drastically help your putting stats.