Just as a general career progression, I would suggest gaining some system administration certifications such as the Microsoft certified program - it's so common that employers ask for MCP/MCSE/MCITP that it's just worth the work anyway. You can self study using virtual machnes & MS Press books and it would go a long way on your CV.
In terms of the job though, it sounds like you've got adequate experience to at least apply for the Network Manager role. Technically make sure you've got a sound knowledge of AD (and how it works in relation to your RM network), DNS, DHCP - ie. the fundamentals of a network. Also start to think about how you would manage a network and the responsibility of line management to get "your head in the right place". Understand the need to document procedure, audit everything (lol).
It doesn't sound like you're falling short at all - you're on the right path