Construct is capable of attaching to a database. There is a tutorial on how to setup and connect to a MySql database here:
https://www.scirra.com/tutorials/525/si ... l-database
To be able to do it, you will have to have some understanding of php and MySql and will need to have a hosted php site with a MySql database accessible from where ever your players are connecting. Assuming you have those 2 requirements, you should be able to follow along with the above tutorial rather easily.