Why does my coconut sauce lack a strong coconut taste?
Canned coconut milk is the base of the majority of savory coconut sauces, Thai or otherwise. It tastes of coconut, but it isn't strongly flavored. If your coconut milk separates (some do, some don't; added emulsifiers inhibit this separation) the thicker layer that rises to the top is coconut cream. Basically coconut cream is coconut milk with less water and more fat. The cream is somewhat more intensely flavored of coconut than the milk, but alone it may be too thick for a lot of sauces.

Coconut milk is made by cooking the meat of the coconut (usually in water, sometimes in dairy milk) and then straining the coconut meat. It is not coconut water, coconut water is the juice that flows out of a just cracked coconut.

Do not confuse coconut milk or coconut cream with cream of coconut, which is usually sweetened. That ingredient is often called for in desserts, but not for savory cooking. Think Pina Coladas. This is a source of some confusion as different countries use different terminologies. Wiki certainly is not the best possible source, but if the language I am using here differs from your understanding of the terms, read this from wiki. Those are the definitions I am using in this answer.

The quality of canned coconut milk varies. It also is available in a "light" formulation, which tastes less strongly of coconut than non-light versions. 

One traditional method seen especially in Thai cooking involves "cracking" the cream. Choose a non-light canned coconut milk without added emulsifiers (check the label). Refrigerating the can overnight can sometimes help separate the cream, figure about the top third of the settled contents of the can. Simmer that cream on the stove until the oil separates, it may take as long as ten minutes. The oil separation is the "cracking". Now you can fry the spices of the sauce (curry paste especially) in the oil (no need to remove the non-oil solids). Add the rest of the can of milk and simmer for a while to reduce the sauce to your desired thickness. Some meat can be cooked in the sauce, vegetables are usually par-cooked separately.

[EDIT: This video shows Cracking Coconut Cream at 2:20 ---
This video shows an alternative, for those that have difficultly getting their cream to separate at 4:10]

Beyond that, to get more coconut flavor you can add coconut powder (which is dried coconut milk) or coconut extract (here's a fun recipe from Alton Brown) but neither of those additions would be traditional.