I don't think Neo couldn't carry his martial arts skills to the real world. It is true that he learned them inside the matrix and they were more programmed into his brain rather than learned the "traditional" way. But if there is one thing that is the same in both the real world and the matrix, it's Neo's brain, since that is how he's connected to and existing in the matrix. So he learned all this into his actual brain, no matter if just electronically (in the end he also learned to speak in the matrix, yet can speak right away in the real world, ...).
And while martial arts are an inherently physical activity, many aspects are just a matter of learning and done mainly through the brain, I think. So while Neo might not be as phyisically trained as in the matrix and might not have as fast muscular reflexes, he nevertheless knows all the moves and has the same abilities of anticipation.
(And apart from that, how often have you seen somebody stand the chance against someone else far more capable in the movies. There are really much larger inconsistencies in the matrix trilogy. In fact Neo carrying over his martial arts skills into the real world is far more believable than him carrying over his "magic skills" from the matrix.)