Here, some means
some
1. being an undetermined or unspecified one
So there isn't an issue regarding plurality: justification can be singular.
You can use justification as a plural like you would with good reason.
Here is an example in the same sense as your example. I don't know why there were budget cuts. There must be some good reason for the recent budget cuts →
- There must be some justification for the recent budget cuts.
There can also be multiple undetermined justifications. I don't know why there were budget cuts. There must be some good reasons for the recent budget cuts →
- There must be some justifications for the recent budget cuts.
If there is just one justification for a particular action, then justification (singular) is correct.
- We have just one justification for the recent budget cuts.
If there are more than one reasons for a particular action, then justifications (plural) is correct. For example, imagine that there are ten reasons for the budget cuts, but only three are presented: here are some reasons for the recent budget cuts→
- Here are some justifications for the recent budget cuts.
Here's a headline I found online that uses justifications.
18 Solid Justifications for Cloud Computing -- and 10 Situations Where It Doesn't Work