You did just exactly what you thought you did. All you can really do is get a heavy grit and take the top down to equal depth. Then go with a finer grit and a finer grit till you're happy with the surface.
I have a belt sander that makes a job like that last about ten minutes. It takes longer to change belts than it does to sand a surface. With a palm or orbital sander it'll take forever, but it is what it is.
Regardless, once you stain, the wood is liable to take up stain differently, especially if it's pine. Knots and pitch pockets laugh at stain, but that does look more "natural" than a spot you dug out with a sander.
The reason I mention it is that you may go through all the extra work only to end up with the same results. If you can live with it, leave well enough alone.
You can also try to stain the rest of the table less the spots and see if they'll take a heavier color, but I wouldn't expect too much.
Good Luck!!!
