Dark energy, dark matter, and gravity are intimately entwined concepts, certainly. The question seems to blur dark matter and dark energy together or use the terms interchangeably, but they are separate theories attempting to reconcile separate discrepancies.
One facet contributing to the majesty of Einstein's Equations for gravity (see http://en.wikipedia.org/wiki/Einstein_field_equations, particularly the form given just before "Sign convention") are that they are all-inclusive- curvature is mass-energy, mass-energy is curvature. The equation begs to be enlarged and expanded to include the entire universe, and thus it is the foundation of modern cosmology.
As such, Einstein's Equations describe how the Universe should expand, deform, warp, or contract (if it had enough mass) given its content of mass and energy. Dark energy is part of the nascent attempt by theorists to reconcile what matter we can see with the largest-scale behavior as observed. Gravity as we are traditionally familiar with it is always attractive, so any collection of objects moving apart from each other should at least be slowing down, if not actually turning around and colliding. What we see on the grandest scales, though, is an acceleration. Something fundamental has to be wrong with the traditional picture, and dark energy is a catch-all term for attempts at the modification of Einstein's Equations themselves.
Dark matter, on the other hand, is a catch-all term for attempts to reconcile smaller-scale discrepancies between the observed behavior of objects and the theoretical predictions of their behavior assuming that every object was visible. This is where the alternate term "Missing Matter" comes from. Smaller objects, like galaxies and clusters of galaxies, seen to behave as if there were extra, invisible matter holding them together. It is a less-ambitious correction, since there is no attempt to argue that Einstein's Equations themselves need correction, we merely need some extra matter that doesn't produce any light on the right hand side in order to account for the extra curvature of spacetime inferred from the behavior of observed objects on the left.
I'm sorry if that's not as neat or tidy an answer as you were looking for. Given the deep philosophical implications of both sides of Einstein's Equations being both cause and effect, it is impossible to draw the same kind of distinction between gravity, dark matter, and dark energy as you could between the influences of, say, sunshine and heat from the Earth's core on ground temperatures. Therefore, for instance, there is no "extra" spacetime. Einstein himself discouraged the use of "deformation" and "warping" as they lead to the notion that there is some natural condition for spacetime and matter just messes it all up. Spacetime and matter are like the first two cards of a house of cards- they have to be taken together because either one by itself will just collapse.