I also haven't read the book, so I can only offer my point of view, not analyze C.S. Lewis'
OK, analogies are always dangerous, but I'm going to try one here.
Taking one single choice you've got three participants (there may be more, but we're going to limit it to three for now) : You, God, and Satan. God has created you and given you all you need to make this choice and make it 'right'.
God is on one side giving advice on how to choose. Satan is on the other side giving conflicting advice.
If you choose to follow God, the 'right' choice, then God get's the credit for giving you the choice, the means to carry it out, and the direction on what to do. If you choose the other option then you take the blame for misusing the choice, the means, and listening to the wrong advice.
Now, possible problems with this analogy:
1) You may believe in God, but not the Devil. Well, so instead of listening to the wrong advice you just didn't listen to the correct advice. Still your fault.
2) You may not belive in God. Well, for the sake of this question we're just going to have to make the assumption that He exists, okay.
3) You may not believe that God advises on how to choose. Similar to the first problem, it was your choice and God gave you everything you needed to carry it out. Of course, I don't know anyone that belives in God that doesn't belive that He has given some type of direction on how to live. (They may be out there, I just don't know any.)
I guess the point is that God get's credit because He gave you everything and so anything you do good with it can be traced back to Him. Whereas anything bad is done by rejecting Him.
I think what Lewis is trying to do is get people to realize their dependance on God and how he has given us everything from life to daily breath. I don't think he's trying to say that God doesn't give you credit for the good things you do and the good choices you make.
King Benjamin in the Book of Mormon also explained it this way:
Mosiah Chapter 2:20-26
20 I say unto you, my brethren, that if you should render all the thanks and praise which your whole soul has power to possess, to that God who has created you, and has kept and preserved you, and has caused that ye should rejoice, and has granted that ye should live in peace one with another—
21 I say unto you that if ye should serve him who has created you from the beginning, and is preserving you from day to day, by lending you breath, that ye may live and move and do according to your own will, and even supporting you from one moment to another—I say, if ye should serve him with all your whole souls yet ye would be unprofitable servants.
22 And behold, all that he requires of you is to keep his commandments; and he has promised you that if ye would keep his commandments ye should prosper in the land; and he never doth vary from that which he hath said; therefore, if ye do keep his commandments he doth bless you and prosper you.
23 And now, in the first place, he hath created you, and granted unto you your lives, for which ye are indebted unto him.
24 And secondly, he doth require that ye should do as he hath commanded you; for which if ye do, he doth immediately bless you; and therefore he hath paid you. And ye are still indebted unto him, and are, and will be, forever and ever; therefore, of what have ye to boast?
25 And now I ask, can ye say aught of yourselves? I answer you, Nay. Ye cannot say that ye are even as much as the dust of the earth; yet ye were created of the dust of the earth; but behold, it belongeth to him who created you.
26 And I, even I, whom ye call your king, am no better than ye yourselves are; for I am also of the dust. And ye behold that I am old, and am about to yield up this mortal frame to its mother earth.
I hope that helps answer the question. I think Benjamin explains it better than I do, personally.