What is a critical analysis of this quotation "Don't say that, Governor. Don't look at it that way. What am I, Governors both? I ask you, what am I? I’m one of the undeserving poor: that's what I am. Think of what that means to a man. It means that he's up agen middle class morality all the time. If there's anything going, and I put in for a bit of it, it’s always the same story: “You're undeserving; so you cant have it.” But my needs is as great as the most deserving widow’s that ever got money out of six different charities in one week for the death of the same husband. I don't need less than a deserving man: I need more. I don't eat less hearty than him; and I drink a lot more. I want a bit of amusement, cause I’m a thinking man. I want cheerfulness and a song and a band when I feel low. Well, they charge me just the same for everything as they charge the deserving. What is middle class morality? Just an excuse for never giving me anything. Therefore, I ask you, as two gentlemen, not to play that game on me. I’m playing straight with you. I ain't pretending to be deserving. I’m undeserving; and I mean to go on being undeserving. I like it; and that's the truth. Will you take advantage of a man’s nature to do him out of the price of his own daughter what hes brought up and fed and clothed by the sweat of his brow until she's growed big enough to be interesting to you two gentlemen? Is five pounds unreasonable? I put it to you; and I leave it to you."

Mr. Alfred Doolittle is a minor character in the famous 1912 play Pygmalion by George Bernard Shaw. Even though he appears in only two scenes, Mr. Doolittle is a character through whom Shaw conveys his social and political views. Thus, his monologues and dialogues, despite their comedic and humorous tone, usually carry a deeper meaning. An example of this would be the quote you’ve asked to be analyzed.
Shaw portrays Mr. Doolittle as an amoral drunkard, a working class dustman, a father, and a husband to at least six women; a poor, “undeserving” man who by the end of the play becomes a member of the one socioeconomic class he has always despised--the middle class. He says:

“I’m one of the undeserving poor: that’s what I am. Think of what that means to a man. It means that he’s up agen middle class morality all the time . . . What is middle class morality? Just an excuse for never giving me anything. Therefore, I ask you, as two gentlemen, not to play that game on me. I’m playing straight with you. I ain’t pretending to be deserving. I’m undeserving; and I mean to go on being undeserving. I like it; and that’s the truth.”

Having discovered that Professor Higgins and Colonel Pickering want to transform Eliza into a proper lady, Mr. Doolittle offers his daughter for mere five pounds and asks for the money only to buy more drinks and provide some amusement and cheerfulness for his soul.
With this particular quote, Shaw presents the concept of middle class morality--or the way a person must behave and think when they are a member of the middle class. The middle class must work in order to gain the wealth they deserve. Mr. Doolittle would rather be a poor man than belong in the middle class, because then he won’t have to live according to the morality and ethic of said class.
Being poor and undeserving of his wealth means that he won’t be required to provide for the other people of the society who’ll come to him asking for help and money, and he won’t have to change the way he speaks, the way he acts and the way he looks. He won’t have to worry about anything he does nor will he have any important societal responsibilities and obligations, because the rich and higher classes won’t even bother to acknowledge his existence. He’ll be living by his own rules, morals and principles simply because he can’t afford the morals of the middle class.
Essentially, Shaw portrays Doolittle as a representative of the entire lower class: those who live in poverty and those who must work to survive, and uses him as a platform to present the real meaning of morality and social equality.
Shaw was a Fabian socialist, meaning he believed that democratic socialism is an ideology and a political system that can be achieved gradually, through an evolutionary process, unlike the violent and revolutionary doctrines of Marxism. Through Mr. Doolittle’s monologue, Shaw expresses his own criticism of the society and his opinions on the socioeconomic classes, and explains how money and wealth can completely transform a person, both physically and psychologically.