A 4-engine plane can safely fly with one shut down, however, when you have dozens of airports around you, drop an engine and decide to still head out over thousands of miles of cold ocean, I fail to understand why the Capt did not choose to turn around.
The cause of the failure was determined after the jet landed.
Sure, it's inconvenient and expensive to turn back, but how could he be so sure the remaining engines would not experience any issues and commit his passengers lives to that assumption for several hours, without knowing 100% why the failure happened.