After asking about how Neo could use his powers outside the Matrix, it left me thinking about this from another point of view.
While there is a question about how Neo could use his powers outside the Matrix, there is another question that comes with that: How did Neo know his power would work on the weapons the Machines were launching at him and the ship?
Neo knew the difference between inside and outside the Matrix, and knew the difference between reality and the fantasy world in the Matrix. On the surface, he had no reason to expect his powers to work outside the Matrix. Something must have given Neo a reason to believe his powers worked in the real world.
What make him think his powers would work against the Machines outside the Matrix?