I may have misunderstood and as Sidewinder says, is the gap between the bottom of the neck heel and the top of the pocket?

If so, it sounds like the neck wasn't sitting fully flush against the pocket when you started screwing it on. The screws had then reached the end of their travel through the body before the neck was pulled down tight.

As Sidewinder says, it's very likely that the same sized drill was used to drill the body and neck mounting holes. It makes sure things line up, but for the joint to work well like that, the neck really needs to be clamped firmly to the body when fitting the screws. It's much better (and easier) to enlarge the four body holes (not the neck ones) so that the screws now are now a tight push fit through the holes and don't require screwing through. This ensures that the screws can pull the neck right down to the body nice and tightly.

If you leave any gap between the neck and body when screwing using the same sized holes, then the screws will always come up tight against the body and not turn any further before they've pulled the neck right down. So drilling the body holes out to just the outside diameter of the the screw makes sure that this doesn't happen. Don't make the hole any bigger than this, otherwise the screws and the neck can then move around. So same size or just very slightly under. The tighter the fit without having to actually screw the screw in, the better.