In both Charlie and Algernon the same process has been carried out in which intelligence is artificially increased, though the result is not permanent. Charlie experiences life as a brilliant man, then has to suffer a reversal of the change in which his intelligence level begins to decrease, and he once again becomes mentally disabled and awaits his probable death, just as has happened to Algernon.
Your question brings up the issue of what animals are capable of experiencing both intellectually and emotionally. The poignancy of Charlie's story lies in his awareness of what is happening to him as the process reverses itself and he realizes he'll become what he once was, a man who is (in the parlance of that time) mentally retarded. From the standpoint of emotion and self-awareness, Charlie would have been better off if the experiment had never been carried out and he had never been given a chance to experience life as not only a mentally "normal" person, but a genius as well.
Can a mouse, or any animal, feel the same sense of loss and impending doom that a person feels ? The famous poem "To a Mouse" by Burns reflects our conventional assumption that this is not so, and in Burns's view this is to the mouse's advantage:
For thou art blessed, compared with me,
The present only toucheth thee.
But och ! I backward cast my eye
On prospects drear,
And forward, though I canna see,
I guess and fear !
Yet none of us can know the inner mental experience of an animal. The fact that animals do not possess language, the chief element of communication from the human perspective, has made us assume that they cannot think on any but the most rudimentary level. But how do we know this ? A secondary question relates to Algernon's intelligence having been artificially raised to a level not possible in the natural environment. So the possibility does exist that Algernon has been able to feel the same level of loss, regret, and terror of both the reversion to his former self and his impending death, just as Charlie tragically does.