The Doctor likely had a small reserve of regeneration energy left but not a sufficient amount to fuel a complete regeneration.
Time Lords have a finite amount of regeneration energy. When used properly and appropriately, that energy can allow a Time Lord to have up to thirteen distinct incarnations.
(It is worth remembering that Time Lords don't necessarily reach that total as evidenced by the Tenth Doctor's actions in Journey's End/Stolen Earth. The Doctor, for example, only had twelve distinct incarnations but still regenerated twelve times.)
This does not necessarily mean that this exhausts all of a Time Lord's store of regeneration energy. Indeed, there is evidence to suggest that a Time Lord can retain just enough energy to induce a thirteenth regeneration but these are evidently fatal. Azmael, a renegade Time Lord, did just this and consequently died.
You could therefore postulate that the Eleventh Doctor, having regenerated completely twelve times, may also have had just enough left to do what he did to River in The Angels Take Manhattan.