From my favourite vegan cookbook, How It All Vegan by Sarah Kramer and Tanya Barnard. Seems pretty close to what you said you did... if you're looking for more 'basic' you could maybe leave out the basil (?)
1 6-oz can of tomato paste 1.5 tbsp vinegar 1 tbsp sweetener 1 tsp Braggs or soy sauce 1/8 tsp dried basil 1/8 tsp paprika 1/8 tsp salt 2.5 tbsp water
In a med. saucepan, simmer all the ingredients on med-low heat for about 10-15 mins, stirring often. Set aside to cool and store in the fridge in a clean, dry container with a tight fitting lid. Keeps about 2 weeks but make sure the lid is kept on tightly. Makes about 3/4 cup.