Welcome to the Community,
please take a look at http://www.virten.net/2013/09/esxi-5-x-installation-on-intel-nuc-fails-with-no-network-adapters/ for information on how to customize the installation image to recognize your network adapter. When you install ESXi as a VM in VMware Workstation, it's not the physical NIC that's presented to the VM, but a virtual NIC for which ESXi has the drivers built-in.
André