That is correct. You would not be able to use the relay outputs.
The Nano-10 is technically rated for 24VDC only; however, it can actually be run on 12VDC if you have no other option but is subject to the following conditions:
1) Outputs 3 & 4 (relays) will not work, so only outputs 1 & 2 are available.
2) The PLC cannot implement the power failure interrupt. (PFI occurs at around 15 to 17V, so it won't work). This is a special type of Interrupt described in the Interrupts section of the Nano-10 user manual.