External hard drive (Seagate) lost after power cut

As mentioned the drive has likely failed. If you have access to another Mac connect it and if the drive still cannot be seen that verifies the issue. If you don't another Mac available, then take the EHD to someone (a friend, an Apple Store or AASP, or even a retailer like Best Buy) and try it there.

Try this: How to reset the System Management Controller (SMC) on your Mac ...

Your external drive may have failed due to the stress of a sudden power outage. Going forward after replacing the drive consider getting a Uninterruptable Power Supply (UPS) for your computer and the external drives. You can find them at your local office supply stores or if you have a Batteries Plus in your area they are available there.

Personally I use an older one made by APC, the ES750. If you don't know what a UPS is please look at https://en.wikipedia.org/wiki/Uninterruptible_power_supply

BTW, I would also recommend using an OWC (www.macsales.com) external HD. You can find them at:

OWC Mercury Elite Pro: Production-Grade External Hard Drive many experienced users on these forums use them due to their extreme reliability and reasonable prices.