Ah yeah, I know that problem too well. You're probably playing with a keyboard, right? Now a keyboard button has only two states: "pressed" and "not pressed", so if you press the button, the responsible input variable directly goes from 0% to 100%, while an analog stick allows for a much smoother transition (I think mine has 8 bit/axis=256 different states).
So the only way to "fix" this is to buy a USB controller for your computer. Most of them have a PS2 controller layout, so you don't have six buttons on the right (only 4 which I normally use for A, B, Z, Start), but you can assign the C-Buttons to the D-Pad (on the left). With that setup it's really easy to beat most N64 games. Such controllers start at ~15$, you can get quite decent ones (with Precision Aim etc) for around 30$. Of course you can also buy an original N64 controller or use yours if you have one and buy an additional N64->USB converter for around 30$.
If you're on Project 64, most controllers seem to be supported (version 1.6 and higher) if properly installed in Windows. You can even enable rumble effects!