As long as it doesn't last for days, you'll be fine. Oxygen is dissolved into the water along the surface of the tank. It always works like that, but using filtreation/aeration 'mix up' the water so more is at the top to take in the oxygen.
Really, what can you do? Unless you want to go out and spend the money for a battery backup system, or battery powered filter and air pump - there's not much that can be done withoug power.