Look and see. If there is just a pump and tire goo plus the plastic funnel so you can add things to the cap less gas tank, then you don't have a spare tire . A spare wasn't even an option for my 2011 v6. I ended up ordering a new spare for a 2010 GT with a jack for almost $500 from my local Ford dealer . I believe it is a $200 (just a guess) option now.
Sorry to hear you don't have a spare. Mine's very small and would look crappy but gets the job done. I also had an issue one time where my alert said I had low tire pressure. I checked all 4 of my regular tires and they were fine. I checked the spare and it was a little low. I find it funny and cool that the car can actually notice that too.. not sure how, but after airing it up the alert went away.