The warning is a little out of date - I've changed it for the next build to warn you if your image size exceeds 2048.
All modern devices, even mobiles, can handle images sized 2048x2048. However images larger than that are not supported everywhere, and will be unable to play the game if you try to use a bigger image. So the absolute maximum is 2048x2048 - never make a single image which exceeds that size.