The saddle height and fore/aft position is usually set for efficient pedaling with a bit more latitude in the fore/aft adjustment. Soon some will opine, probably accurately, that you need to strengthen your core. I'm sure that's important, but your handle bar height, reach and angle can also have a big effect. I don't ride straight handlebars, but if your wrists aren't in a natural position, no matter the type of bar, then you could be affecting the nerves in your hands or wrists. I've also found that handlebars too high puts more pressure on my hands by not allowing me to engage the supporting muscles; I see a similar issues when are bars are a bit too close.
Also agree that the saddle tilt can create additional pressure - very small changes in this can transition a rider from sliding forward to "just right" to "ouch".