Q:

Why would Director Krennic be held responsible for the breach on Scarif?

Tarkin believed that Krennic was partially at fault for the breach on Scarif:
From Tarkin's Point of View:

Director Krennic, General Ramda, and Admiral Gorin had all failed to solve the problem at hand, granting the rebels opportunity after opportunity to seize the schematics from the Citadel.
It was a show of incompetence so great that Tarkin was almost curious to know how Krennic might explain it away.
Rogue One: A Star Wars Story, Chapter 21

But Krennic's position is closer to a supervisor of military projects than a commander. His life is outlined in Catalyst and the Rogue One Ultimate Visual Guide:

First, he studied Architecture at the Futures Program:

When Krennic was a young man, his brilliance earned him a place inthe Brentaal Futures Program, an educational institute meant to incubate developing prodigies. Young Orson's listed area of excellence was architecture.
Rogue One Ultimate Visual Guide, page 108

Then, he joined the Corps of Engineers, reconstructing Coruscant and supervising construction projects:

During the Clone Wars, it was Krennic who oversaw the transformation of municipal grounds on Coruscant into military command centers.
Rogue One Ultimate Visual Guide, page 108
... he had risen quickly to the fore in the Republic Corps of Engineers, supervising the construction of enormous projects ...
Catalyst: A Rogue One Novel, Chapter 6

Next, he was transferred from the Corps of Engineers to the Strategic Advisory Cell, requiring him to become a weapons expert:

Recently transferred from the Crops of Engineers to the cell's Special Weapons Group, ...
The new assignment had also required a