The database server is in the computer I used in creating the standalone exe file.
If so, the computers running the application needs to have access to the computer where you created the application, and the connection string must point to that computer.
You need to understand that SQL Server applications are client/server applications. Your standalone program is the client. There is nothing in that program which includes SQL Server. SQL Server always runs in a separate process. And in many cases it runs on a separate computer from the application. You can imagine an application used in a corporation with thousands of users. The users have the application on their laptops, but there is only one instance of SQL Server running on a server somewhere in the IT Centre.
Presumably the idea in your case is that user should have the database on his or her computer, but then that computer must have SQL Server installed. You could include this in the installation of your application.
If you want all bundled in a single executable, there are other DB alternatives that are more lightweight and better suited for this low-end part of the scale. SQLite, for instance, is quite popular.