Way to recover the undertale genocide route after fighting mettaton NEO

There's no need to count the number of enemies in each area. Just keep killing enemies in the area until you get the "But nobody came" message in your random encounters. This means you have killed all the enemies in this area and you can continue on to the boss. Be sure you finish this before approaching the area's boss, even if you can normally go back before actually fighting them.

Save points outside the Ruins also have a counter indicating how many enemies are left in the area.

When doing a Genocide run don't forget killing the dummy and the initial Froggit.

You can view a full list of all the enemies you need to kill here.

There's nothing stopping you from leaving the final area before the Asgore fight.

In fact, before the first attempt at the fight, Asgore even gives you an opportunity to go back for anything else you needed to do. I'm not sure how you're getting lost going back, since it's a completely linear path back to the Core other than the elevator shortcut.

Either take the first elevator you see and then continue south until you reach the elevator back to the Core, or ignore the elevators until there's nowhere left to walk. This will take you back to the end of the Core. The elevator just outside the Mettaton battle area will lead you back to the first room of the Core. Simply continue south from there to get back to MTT Resort, where you can find a shop, or continue out elsewhere for other shopping options or sidequest activities.