The Red Sox problem is that it is very difficult for them to be able to upgrade their roster over the guys who will be returning from the DL. The rotation, even with Dice K, should not be terrible. If Morales can continue his magic, he could be a big boon to the rotation. Bailey will be returning to the bullpen. Melancon looks to be straightened out, and maybe Bard can return to being a useful bullpen piece.
When Ellsbury, Crawford, and Ross return, the lineup should be potent with Kalish and Middlebrooks etc.
However, by the time these guys get back, it may be too late to make a run at the division because the Yankees are putting some distance between themselves and the Red Sox. The Sox need to keep close to the Yankees. If they are 15 games behind at the All Star Break, they can forget the division. They be playing for a 1 game playoff with a wild card berth.
They are caught in-between in this waiting game. There is nothing they can do but try to win as many games as possible with this skeleton crew and hope the Yankees hit a skid.