Most of the time when you putt, your face is down so that you aren’t looking at the hole. Golfers often practice their putts this way as well.
If you were to roll a ball to the hole, wouldn’t you keep your eye on the hole to get a feel for it? Why don’t you apply this same principle to your putting?
With your putter, turn your head to the hole. Take 4-5 practice strokes while looking at the hole. Then, as you putt the ball, keep your face down and try to replicate your practice strokes. This will help you roll it within a 2-3 foot radius.