It’s not so easy to create a good user interface. A key consideration is to meet user expectations.
And user expectations are very much bound to the context/environment of the program. For example, if you start using „Windows shortcuts“ like Ctrl+C and Ctrl+F on a Mac you’ll surely break users expectations. Same thing goes for text operations.
These and many more are features you’ve come to expect won’t accept if they were taken away. By the way, if a functionality is not found in its expected location, it doesn’t exist. This sounds harsh but most users won’t take the time to figure stuff out.
Odd enough, web apps seem to be a category on their own. User expectations (at least from my limited point of view) seem to vary widely using a web app in comparison to a native app.
So take a moment and get to know the expectations set for the target system. Here are the links to the user experience guidelines for OS X, Windows 7 and Windows 8.