The rules are you friend here.
Rearrange your face in to a robotically compassionate arrangement and press play
''well, the rule is......
We're operating within the guidelines here, as we must........
The handbook says .........
Policy states
The council says .........
Legislation says......
If it's a bit vague, say ''well, people many grades above me have decided that...''
You're basically just the mouthpiece for decisions that have been made by people above you and you're unapologetically passing this on. With a sympathetic face.
You'll know yourself how to tweak these, but basically, staple gun on your half smile half robot face and reiterate calmly that these are the rules, this is how it is.
If anybody has a go at you after you use this line of defence then move on to line of defence two, ie the rules are to protect you.
I work in one of these roles, constant stream of people lining up to complain and it does require a resilience which I know I didn't have a decade ago.