How to properly phrase "can't fall back on anyone"
You may want to try any of the following terms:
- unassisted
- solely responsible for (task)
- without backup
- only resource for (task)
- single point of failure (although this could be considered to reflect negatively on your manager, as these are to be avoided in business)
I would probably chose 'solely responsible' since it emphasizes your positive attribute (responsibility for something important) more than the negative of your manager (failing for provide backup for something important).