From your description, the "thing missing" that jumped out at me was salt.
Also, spices and herbs help give a better, more familiar taste.
I've made basic sauce from tomato paste, since it's easy to keep and store - and once I have the can open, I would rather use it than wait for it to go bad while I open a separate tomato sauce. Salt for me is usually the catalytic that makes it go from watery paste to sauce-flavored, for me - and it takes a bit before the result stops tasting watery.
Usually, I'm making just a little bit at a time, maybe a half a cup or so (for tortilla pizzas or the like). I usually mix about equal parts paste and water, add a half teaspoon or so of salt, and some dried herbs, whatever I have on hand (italian mix, garlic or onion powder, basil, whatever). I mix well, let it sit for a while to hydrate the herbs, then taste to get a rough idea - usually I end up adding a bit more salt, sometimes more herbs (depending on how flavorful I want it), adjust the thickness with paste or water. I'm pretty handwavy about exact proportions, but that should hopefully get you within taste-and-adjust distance of your desired sauce.
I don't usually cook the sauce by itself, because for my use it will cook in the dish - but if you're making it by itself, in larger quantities (say for pasta), you should probably cook for a bit on stove-top to let the herbs and spices cook into the sauce and let the flavors meld.
If you wanted, you could add other ingredients to your sauce to get the flavors you're looking for - garlic, onion, carrot, and celery, sugar, olive oil, fresh herbs, anything you want. But if you're looking for a basic sauce of tomato paste, water, and sugar... just add salt and keep adding till it starts tasting like sauce.