You sure can. The way to do this would be the following:
1) Create an account for the people in your company that will be uploading documents. I'm assuming you already have a login and password, so you can use that one. A hack would be to use a 'company login', but that would not be recommended. It is better that everyone have their own login
2) Create a workspace for each customer. Call it something that your customers can relate to
3) Share the workspace with your customers. The caveat here is that the sharing email has to be sent to an address that your clients use to login. If you don't know what login they use, they will be able to sign up quickly so it shouldn't be much of a problem.
4) Each customer will now only be able to see the workspace you have shared with them. You can drop the files in the workspaces
Hope this helps. Let me know if you have any problems