First of all, please note that Turkey was not a country during WWI. It was the Ottoman Empire, and not Turkey, which participated in WWI on the losing side.
The fact that the Ottomans were on the losing side led to the break up of their empire. The Allies broke up the Ottoman Empire, taking pieces for themselves. Officially, these lands were not taken as colonies but rather as "mandates" to be governed under the auspices of the League of Nations.
After having most of its empire taken away in this manner, the Ottoman Empire was badly weakened. When Greece invaded it after the war, Ataturk and his followers dissolved the Empire and created the Republic of Turkey.