There is no way to disable the Inspect Element feature or the Developer Tools feature for a website.
You can obfusticate or minify your code in order to make it much harder to read and comprehend. Other than that, no.
(Inspect a GMail element for an example of obfusticated and minified code)
Tools like Closure Compiler and Closure Templates can help you with that.
Note that native applications have the same issue. Anyone can (illegally) disassemble your application and read the obfusticated code). I believe it is even easier with .NET and Java (unless the code is obfusticated before the compilation), or any other language compiled into some intermediate form.