What voltage is the supply running at, when you say "supply" do you mean the mains? It sounds like you need a diode on the supply or a transistor/relay that can disconnect from the mains when it goes out and reconnects it when it comes on, but a diode would provide the easiest solution but there is always a voltage drop associated with diodes, so a relay switch or series of transistors may be a better option. A little more description about your setup could be enlightening as well.
I take it you're trying to prevent putting the inverter output from back-feeding to the mains. This is a safety concern for any "generator" as putting power back on the circuit could harm people working on the outage since wires that should be dead could be live do to your inverter, not to mension devices drawing that power could blow a fuse. Setups like these are required to either disconnect entirely from the mains or to be outfitted with a grid tie inverter, those really are your two options.