The main 'issue' (not really an issue though) that I have with the depth is due to the divider lines in your submenues:

When you remove the lines, the depth looks much more realistic, because there are less levels to it:

So instead of lines with a shadow, you could have plain solid ones:

The main 'issue' (not really an issue though) that I have with the depth is due to the divider lines in your submenues:

The drop shadow is underneath the lines, when it should be on top (with some transparency applied to it), which causes the lighter line to appear even lighter.

I'd try that first, moving the shadow to the top. However, something else that might help is to get rid of some of the lines complexity. When you remove them entirely, the depth looks much more realistic, because there are less levels to it:

So instead of lines with a shadow, you could have plain solid ones: