The cosmological constant can be an explanation but it's not an altogether satisfactory one. The Einstein field equations have, essentially, only three parameters: c is the speed of light and is, in some sense, not a parameter but just a scaling factor (it tells us what a second is in metres). G is Newton's gravitational constant, and it tells use how strong gravity is as a force. And finally Λ (big Lambda) is the cosmological constant and tells us something about how the vacuum behaves.
All of these constants are things you need to measure: nothing tells you what G should be except going out and measuring it, and the theory gives no reason for it to have any particular value (well, if it was zero the theory would be vacuous).
The same thing is true of Λ: it's a parameter of the theory which needs to be measured. For a long time, on grounds that turned out to be rather spurious, Λ was assumed to be zero, but as with G the theory doesn't have any opinion on what it should be, and you need to measure it.
So, both G and Λ are things that you need to measure, and if you are happy that G is just some unexplained parameter, then you really should be happy that Λ is as well. Of course, really it would be nice to explain both of these in terms of some other theory since we kind of know that General Relativity can't be a correct theory in various limits. But, on the other hand, people like theories with a very small number of free parameters because they are so hard to adjust to fit the data: if you have a mass of free parameters you can tweak your theory to explain a huge range of phenomena, which means it is very hard for your theory to be wrong: it turns into something Ptolomaic where you can just keep adding epicycles (free parameters) and the theory can never be wrong. And two or three free parameters is a very small number (the standard model of particle physics, for instance, has 19 I think): it's really the smallest number such a theory can have, so GR is quite compelling in that respect.
(The spurious grounds for assuming that Λ should be zero were essentially that its original use was to try and support a steady-state model of the universe, where there is no expansion or contraction. And it won't do that: although you can adjust Λ so that the universe does not expand or contract, the solution isn't stable: any tiny perturbation will cause it to either start expanding or contracting. So, in fact, GR, even with Λ, makes a strong prediction that the universe is either expanding or contracting. This was not known at the time GR was created, and Einstein didn't trust his own theory enough to make what would have been a very bold prediction about the large-scale structure of the universe. If he had done so he would, no doubt, have won a second Nobel prize for it, as the prediction turns out to be true. Instead he decided that, since Λ would not support a steady-state model it should be zero: but there is no reason to assume that at all.)