In order to put a product on sold out, the capacity of the product pool has to be minimized to the sold amount of tickets.
Minimize the product pool to the sold amount of products
Go to the specific product within the Backoffice and scroll down until the 'Product pool'. Here you can see the minimum amount the pool size has to be. The current pool size should be minimized to this amount. Once these settings are saved, the product will be shown as sold out, as there are no more units available.
If you don't know how to edit a product, please see this article.