It is normal for yogurt to be a bit thin the first time you make it, It gets better and then good about the third time
I make homemade yogurt all the time (using raw milk that we buy at a nearby farm). I do 2 things to help thicken it up -- I let it sit in a warm spot wrapped in a towel for at least 12 hours, and before I jar it, I pour off the whey that is sitting on top of the yogurt. (I'm pretty sure it's whey.)
Someone might want to pipe in here, but I believe Greek yogurt is made by draining off excess liquid. I made Icelandic skyr once, and it's done pretty much the same way, although with the recipe I used, I added rennit.