After doing some more digging on Google I found this Vmware documentation that resolved my issue:
1 Power on the virtual machine.
2 While Windows NT is booting, insert the Windows NT 4.0 CD in the CD-ROM drive.
3 Log on to Windows NT and install the AMD PCNET driver:
a Open the Network properties page by double-clicking the Network icon in Control Panel. Change to the Network Adapters screen by clicking the Adapters tab.
b Click the Add button and select the AMD PCNET Family Ethernet Adapter from the list.
c A message pops up prompting you to enter a path for the Windows NT files. Specify the \i386 folder on the CD in the path you enter (for example, type D:\i386 if the CD is in drive D) and click Continue.
d Windows NT setup prompts you for the Windows NT files again. Click Continue.
e Use the default adapter settings; they do not need to be changed. Windows NT setup prompts you again for a path to the Windows NT files. Click Continue to finish installing the driver.