Anything you make in a cheap filter drip coffee machine is going to have an upper bound of how well it can taste. It's a convenient method to brew larger quantities of coffee at once, but not really an ideal way of getting the best tasting coffee.
You might want to try a more medium roast instead of a dark roast and see if that tastes less like dirt to you, but a lot of cheap coffee is going to be dark roast because it hides the taste of the (shitty) beans used.