No, it's not really carbonated, it has CO2 in it, it's not the same thing.
The process of carbonation is when a large amount of co2 is forced into solution, via either force carbing with a keg, OR The yeast eat the sugar solution you feed them. They "fart" co2.
The CO2 gets trapped in the bottle, so it has a couple choices...blow the top of the bottle (the cap) Blow up the bottle, or seek the path of least resistance and dive back into the beer, and get absorbed (carbonated) by the liquid. Since the cap is pretty tight (and ingenious in it's design) and most bottles don't have any flaws and can maintain the pressure, the gas more often than not, takes the third option and goes back into the liquid and is absorbed by it.
What you have is just a tiny amount of co2 in there from fermentation but not the same thing.
In fact wine makers talk about it all the time, they talk about degassing to release it. You need a very very tight place like a keg or a bottle and a lot of co2 farting/volume of liquid in the space in order for it to carbonate.
Just relax....if you are taking a reading just tap the hydrometer test jar a few times.