I unwrapped a simple plane and applied the following 80x80 pixel picture:
Yes, it's quite small. The problem is, the result is all blurry, like so:
How do I make it accurate to the pixel?
If you are using Blender Internal Render Engine: In the Properties Window > Texture Tab > Image Sampling Panel > Filter change it to Box.
Have in mind that this will not have any effect in the viewport preview, but it won't appear blurry in your final render.
If you are in Cycles/EEVEE Render Engine: In the Node Editor, under your material node tree navigate to your image texture node and set the second pull-down menu Interpolation to Closest
Using Blender Render, go into the Materials/Texture//Image Sampling and deactivate the Interpolation checkbox.
For the Filter you probably want Box, FELINE, or Area. I'm not sure exactly what the algorithms behind them are, but the results from EWA are not even remotely sharp. They only differ when a rendered pixel is on the boundary between two pixels of the texture.