Two reasons. First the world is in an oversupply condition relative to current demand. Small interruptions in supply don't leave the global demand searching for more oil; it is readily available without significant price jump.
Secondly, Syria today is rather insignificant in their share of the global oil supply. A lot of what they were producing a couple years ago is barely trickling out already.
There is an oil pipeland that runs along the golan heights from jordan, i think, to the med. Even during the ‘73 war it was pumping oil.