Does one need to make amends for a bad-action done accidentally?
You say "unintentionally" but your friend might see it as "negligence".


I didn't mean to break it!
Yes but you should have looked where you were going! No one else broke it...


I suspect that Buddhism might classify negligence too as volitional, karmically active, and a cause of suffering.

Anyway, I think that arguing about it with the friend probably counts as intentional.

FWIW a civil court might try to apportion blame e.g. based on where the vase was placed. Who knows, maybe it would be appropriate to share the blame.