Mana is important, as well as mana efficiency.
But the instances should be doable, with an adjustment to healing strategy.
I mean, the game is balanced around one-player per toon.

We cannot just spam Flash Heal on a Priest, like we could pre-Cataclysm.

I'd imagine those who adapt to the changes are successful.
And those who cannot change, are whining on the Blizzard forums.

There are quite a few videos of instances being cleared, so they are doable.
I've not tried any, so cannot say what needs to be changed.