First, it must be firm and stable enough to keep the cue solid though the stoke. If the bridge hand moves or is loose it will cause a lack of control that will cause negative reactions (when the cue tip deviates "off line" after contact), especially under pressure.
When under pressure we tend to "tighten up", so I recommend holding the cue firmer under critical conditions. There must also be a "groove" established in your bridge so you can feel the cue going absolutely straight. When you get to the point you KNOW your cue is delivered straight and pure through the cue ball your ready to jump up some levels.
The basic foundation of the game is hitting the cue ball straight every time and understanding how this is accomplished physically in your pre shot routine ( I like to call this the "pre connection routine"). The cue ball is the primary target and for the most part you are just "aware" of the object ball once you're down on the shot.
If you get to "object ball conscious" it leads to a disconnection to occur. You know this is happening when you suddenly miss shots for no apparent reason. I will make an edgecated guess that you don't feel "connected" when this happens.
To get maximum feel when you're down on the shot there must be a "visual trade off," where you shift from "seeing" the shot to "feeling" the shot. I describe the experience as "feeling with my eyes." 'The Game is the Teacher'