Please try not to think that a few minutes might have helped.
Whatever caused her death, if it's so sudden and inexplicable, a few minutes probably wouldn't change anything.
But thanks to you, she didn't have to die muzzled in a cage. It sounds like you allowed her to have a peaceful death instead.
The following may sound dull, but I wish someone had told me this: Focus on the time you've had.
Even if it was only a few days, during those days you gave her a better life.
Belive me, that's is all that matters in the end.