Lost Ability to Regenerate Body Parts during the Transition from Amphibians to Mammals
Regeneration of limbs in amphibians is an adaptation where new limbs are generated by dedifferentiated cells. This process is tightly linked to the embryonic program which, in most animal cells, is a difficult program to access once terminal differentiation has occurred (but it's possible, e.g. induced pluripotent stem cells). 

Of note, amphibians have a unique life cycle that includes metamorphosis. It is thought that organisms with more diverse stages in their development may have increased potential for regeneration. Mammals, after birth, do pass through multiple stages of development, but these stages are largely continuous. 

So the quick answer is: mammalian limbs are made up of terminally differentiated cells (and specialized stem cells) with high barriers of reprogramming. They're difficult to reprogram because there hasn't been strong selective pressure to do so. Limb regeneration might seem like a great adaptation, but it doesn't seem to be that important for the success of mammals. Additionally, selection for "maintaining a full set of functional limbs" could evolve many different ways. For example, primates may have evolved behaviors or reinforced anatomy that reduces their risk of injuring a limb. Also, larger animals are probably less likely to have limbs removed just given their size. And if they do, it may have little effect on their reproductive fitness. A legless amphibian probably finds few, if any, mates.

Yun Gates, and Brock. Regulation of p53 is critical for vertebrate limb regeneration, PNAS 2013